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Wednesday, February 4, 2015

Sea level


From Wikipedia, the free encyclopedia


This marker indicating sea level is situated between Jerusalem and the Dead Sea, Israel.

Sea level is generally used to refer to mean sea level (MSL), an average level for the surface of one or more of Earth's oceans from which heights such as elevations may be measured. MSL is a type of vertical datum – a standardised geodetic reference point – that is used, for example, as a chart datum in cartography and marine navigation, or, in aviation, as the standard sea level at which atmospheric pressure is measured in order to calibrate altitude and, consequently, aircraft flight levels. A common and relatively straightforward mean sea-level standard is the midpoint between a mean low and mean high tide at a particular location.[1]

Sea levels can be affected by many factors and are known to have varied greatly over geological time scales. The careful measurement of variations in mean sea levels can offer information about climate change and has been interpreted as evidence supporting the view that the current rise in sea levels is an indicator of global warming.[2][clarification needed]

The term above sea level generally refers actually to above mean sea level (AMSL).

Measurement

Precise determination of a "mean sea level" is a difficult problem because of the many factors that affect sea level.[3] Sea level varies quite a lot on several scales of time and distance. This is because the sea is in constant motion, affected by the tides, wind, atmospheric pressure, local gravitational differences, temperature, salinity and so forth. The best one can do is to pick a spot and calculate the mean sea level at that point and use it as a datum. For example, a period of 19 years of hourly level observations may be averaged and used to determine the mean sea level at some measurement point.

Sea level measurements from 23 long tide gauge records in geologically stable environments show a rise of around 200 millimetres (7.9 in) during the 20th century (2 mm/year).

To an operator of a tide gauge, MSL means the "still water level"—the level of the sea with motions such as wind waves averaged out—averaged over a period of time such that changes in sea level, e.g., due to the tides, also get averaged out. One measures the values of MSL in respect to the land. Hence a change in MSL can result from a real change in sea level, or from a change in the height of the land on which the tide gauge operates.

In the UK, the Ordnance Datum (the 0 metres height on UK maps) is the mean sea level measured at Newlyn in Cornwall between 1915 and 1921. Prior to 1921, the datum was MSL at the Victoria Dock, Liverpool.

In France, the Marégraphe in Marseilles measures continuously the sea level since 1883 and offers the longest collapsed data about the sea level. It is used for a part of continental Europe and main part of Africa as official sea level.Elsewhere in Europe vertical elevation references (European Vertical Reference System) are made to the Amsterdam Pile elevation, which dates back to the 1690s.

Satellite altimeters have been making precise measurements of sea level since the launch of TOPEX/Poseidon in 1992. A joint mission of NASA and CNES, TOPEX/Poseidon was followed by Jason-1 in 2001 and the Ocean Surface Topography Mission on the Jason-2 satellite in 2008.

Height above mean sea level


vertical reference systems in Europe

Height above mean sea level (AMSL) is the elevation (on the ground) or altitude (in the air) of an object, relative to the average sea level datum. AMSL height is used extensively in radio (both in broadcasting and other telecommunications uses) to determine the coverage area a station will be able to reach. It is also used in aviation, where some heights are recorded and reported with respect to mean sea level (MSL) (contrast with flight level), and in the atmospheric sciences, and land surveying. An alternative is to base height measurements on an ellipsoid of the entire earth, which is what systems such as GPS do. In aviation, the ellipsoid known as World Geodetic System 84 is increasingly used to define heights, however, differences up to 100 metres (328 feet) exist between this ellipsoid height and mean tidal height. The alternative is to use a geoid based vertical datum such as NAVD88.

When referring to geographic features such as mountains on a topographic map, variations in elevation are shown by contour lines. The elevation of a mountain denotes the highest point or summit and is typically illustrated as a small circle on a topo map with the AMSL height shown in either metres or feet or both.

In the rare case that a location is below sea level, the elevation AMSL is negative. For one such case see Amsterdam Airport Schiphol.

Difficulties in utilization


1. Ocean. 2. Reference ellipsoid.
3. Local plumb line. 4. Continent. 5. Geoid

To extend this definition far from the sea means comparing the local height of the mean sea surface with a "level" reference surface, or datum, called the geoid. In a state of rest or absence of external forces, the mean sea level would coincide with this geoid surface, being an equipotential surface of the Earth's gravitational field. In reality, due to currents, air pressure variations, temperature and salinity variations, etc., this does not occur, not even as a long term average. The location-dependent, but persistent in time, separation between mean sea level and the geoid is referred to as (stationary) ocean surface topography. It varies globally in a range of ± 2 m.

Historically, adjustments were made to sea-level measurements to take into account the effects of the 235 lunar month Metonic cycle and the 223-month[citation needed] eclipse cycle on the tides.

Sea level and dry land


Sea Level sign seen on cliff (circled in red) at Badwater Basin, Death Valley National Park.

Several terms are used to describe the changing relationships between sea level and dry land. When the term "relative" is used, it means change relative to a fixed point in the sediment pile. The term "eustatic" refers to global changes in sea level relative to a fixed point, such as the centre of the earth, for example as a result of melting ice-caps. The term "steric" refers to global changes in sea level due to thermal expansion and salinity variations. The term "isostatic" refers to changes in the level of the land relative to a fixed point in the earth, possibly due to thermal buoyancy or tectonic effects; it implies no change in the volume of water in the oceans. The melting of glaciers at the end of ice ages is one example of eustatic sea level rise. The subsidence of land due to the withdrawal of groundwater is an isostatic cause of relative sea level rise. Paleoclimatologists can track sea level by examining the rocks deposited along coasts that are very tectonically stable, like the east coast of North America. Areas like volcanic islands are experiencing relative sea level rise as a result of isostatic cooling of the rock which causes the land to sink.

On other planets that lack a liquid ocean, planetologists can calculate a "mean altitude" by averaging the heights of all points on the surface. This altitude, sometimes referred to as a "sea level", serves equivalently as a reference for the height of planetary features.

Sea level change

Local and eustatic sea level


Local mean sea level (LMSL) is defined as the height of the sea with respect to a land benchmark, averaged over a period of time (such as a month or a year) long enough that fluctuations caused by waves and tides are smoothed out. One must adjust perceived changes in LMSL to account for vertical movements of the land, which can be of the same order (mm/yr) as sea level changes. Some land movements occur because of isostatic adjustment of the mantle to the melting of ice sheets at the end of the last ice age. The weight of the ice sheet depresses the underlying land, and when the ice melts away the land slowly rebounds. Changes in ground-based ice volume also affect local and regional sea levels by the readjustment of the geoid and true polar wander. Atmospheric pressure, ocean currents and local ocean temperature changes can affect LMSL as well.

Eustatic change (as opposed to local change) results in an alteration to the global sea levels due to changes in either the volume of water in the world oceans or net changes in the volume of the ocean basins.[4]

Short term and periodic changes

There are many factors which can produce short-term (a few minutes to 14 months) changes in sea level.

Periodic sea level changes
Diurnal and semidiurnal astronomical tides 12–24 h P 0.2–10+ m
Long-period tides
Rotational variations (Chandler wobble) 14 month P
Meteorological and oceanographic fluctuations
Atmospheric pressure Hours to months −0.7 to 1.3 m
Winds (storm surges) 1–5 days Up to 5 m
Evaporation and precipitation (may also follow long-term pattern) Days to weeks
Ocean surface topography (changes in water density and currents) Days to weeks Up to 1 m
El Niño/southern oscillation 6 mo every 5–10 yr Up to 0.6 m
Seasonal variations
Seasonal water balance among oceans (Atlantic, Pacific, Indian)
Seasonal variations in slope of water surface
River runoff/floods 2 months 1 m
Seasonal water density changes (temperature and salinity) 6 months 0.2 m
Seiches
Seiches (standing waves) Minutes to hours Up to 2 m
Earthquakes
Tsunamis (generate catastrophic long-period waves) Hours Up to 10 m
Abrupt change in land level Minutes Up to 10 m

Long term changes


Sea-level changes and relative temperatures

Various factors affect the volume or mass of the ocean, leading to long-term changes in eustatic sea level. The primary influence is that of temperature on seawater density and the amounts of water retained in rivers, aquifers, lakes, glaciers, polar ice caps and sea ice. Over much longer geological timescales, changes in the shape of the oceanic basins and in land/sea distribution will also affect sea level.

Observational and modelling studies of mass loss from glaciers and ice caps indicate a contribution to sea-level rise of 0.2 to 0.4 mm/yr averaged over the 20th century. Over this last million years, whereas it was higher most of the time before then, sea level was lower than today.

Sea level reached 120 meters below current sea level at the Last Glacial Maximum 19,000–20,000 years ago.

Glaciers and ice caps

Each year about 8 mm (0.3 inches) of water from the entire surface of the oceans falls onto the Antarctica and Greenland ice sheets as snowfall. If no ice returned to the oceans, sea level would drop 8 mm (0.3 in) every year. To a first approximation, the same amount of water appeared to return to the ocean in icebergs and from ice melting at the edges. Scientists previously had estimated which is greater, ice going in or coming out, called the mass balance, important because it causes changes in global sea level. High-precision gravimetry from satellites in low-noise flight has since determined that in 2006, the Greenland and Antarctic ice sheets experienced a combined mass loss of 475 ± 158 Gt/yr, equivalent to 1.3 ± 0.4 mm/yr sea level rise. Notably, the acceleration in ice sheet loss from 1988–2006 was 21.9 ± 1 Gt/yr² for Greenland and 14.5 ± 2 Gt/yr² for Antarctica, for a combined total of 36.3 ± 2 Gt/yr². This acceleration is 3 times larger than for mountain glaciers and ice caps (12 ± 6 Gt/yr²).[5]

Ice shelves float on the surface of the sea and, if they melt, to first order they do not change sea level. Likewise, the melting of the northern polar ice cap which is composed of floating pack ice would not significantly contribute to rising sea levels. However, because floating ice pack is lower in salinity than seawater, their melting would cause a very small increase in sea levels, so small that it is generally neglected.
  • Scientists previously lacked knowledge of changes in terrestrial storage of water. Surveying of water retention by soil absorption and by artificial reservoirs ("impoundment") show that a total of about 10,800 cubic kilometres (2,591 cubic miles) of water (just under the size of Lake Huron) has been impounded on land to date. Such impoundment masked about 30 mm (1.2 in) of sea level rise in that time.[6]
  • Conversely estimates of excess global groundwater extraction during 1900–2008 totals ∼4,500 km3, equivalent to a sea-level rise of 12.6 mm (0.50 in) (>6% of the total). Furthermore, the rate of groundwater depletion has increased markedly since about 1950, with maximum rates occurring during the most recent period (2000–2008), when it averaged ∼145 km3/yr (equivalent to 0.40 mm/yr of sea-level rise, or 13% of the reported rate of 3.1 mm/yr during this recent period).[7]
  • If small glaciers and polar ice caps on the margins of Greenland and the Antarctic Peninsula melt, the projected rise in sea level will be around 0.5 m (1 ft 7.7 in). Melting of the Greenland ice sheet would produce 7.2 m (23.6 ft) of sea-level rise, and melting of the Antarctic ice sheet would produce 61.1 m (200.5 ft) of sea level rise.[8] The collapse of the grounded interior reservoir of the West Antarctic Ice Sheet would raise sea level by 5 m (16.4 ft) - 6 m (19.7 ft).[9]
  • The snowline altitude is the altitude of the lowest elevation interval in which minimum annual snow cover exceeds 50%. This ranges from about 5,500 metres (18,045 feet) above sea-level at the equator down to sea level at about 70° N&S latitude, depending on regional temperature amelioration effects. Permafrost then appears at sea level and extends deeper below sea level polewards.
  • As most of the Greenland and Antarctic ice sheets lie above the snowline and/or base of the permafrost zone, they cannot melt in a timeframe much less than several millennia; therefore it is likely that they will not, through melting, contribute significantly to sea level rise in the coming century. They can, however, do so through acceleration in flow and enhanced iceberg calving.
  • Climate changes during the 20th century are estimated from modelling studies to have led to contributions of between −0.2 and 0.0 mm/yr from Antarctica (the results of increasing precipitation) and 0.0 to 0.1 mm/yr from Greenland (from changes in both precipitation and runoff).
  • Estimates suggest that Greenland and Antarctica have contributed 0.0 to 0.5 mm/yr over the 20th century as a result of long-term adjustment to the end of the last ice age.
The current rise in sea level observed from tide gauges, of about 1.8 mm/yr, is within the estimate range from the combination of factors above[10] but active research continues in this field. The terrestrial storage term, thought to be highly uncertain, is no longer positive, and shown to be quite large.

Geological influences


Comparison of two sea level reconstructions during the last 500 Ma. The scale of change during the last glacial/interglacial transition is indicated with a black bar. Note that over most of geologic history, long-term average sea level has been significantly higher than today.

At times during Earth's long history, the configuration of the continents and sea floor have changed due to plate tectonics. This affects global sea level by altering the depths of various ocean basins and also by altering glacier distribution with resulting changes in glacial-interglacial cycles. Changes in glacial-interglacial cycles are at least partially affected by changes glacier distributions across the Earth.

The depth of the ocean basins is a function of the age of oceanic lithosphere (the tectonic plates beneath the floors of the world's oceans). As older plates age, they becomes denser and sink, allowing newer plates to rise and take their place. Therefore, a configuration with many small oceanic plates that rapidly recycle the oceanic lithosphere would produce shallower ocean basins and (all other things being equal) higher sea levels. A configuration with fewer plates and more cold, dense oceanic lithosphere, on the other hand, would result in deeper ocean basins and lower sea levels.

When there was much continental crust near the poles, the rock record shows unusually low sea levels during ice ages, because there was much polar land mass on which snow and ice could accumulate. During times when the land masses clustered around the equator, ice ages had much less effect on sea level.

Over most of geologic time, the long-term mean sea level has been higher than today (see graph above). Only at the Permian-Triassic boundary ~250 million years ago was the long-term mean sea level lower than today. Long term changes in the mean sea level are the result of changes in the oceanic crust, with a downward trend expected to continue in the very long term.[11]

During the glacial-interglacial cycles over the past few million years, the mean sea level has varied by somewhat more than a hundred metres. This is primarily due to the growth and decay of ice sheets (mostly in the northern hemisphere) with water evaporated from the sea.

The Mediterranean Basin's gradual growth as the Neotethys basin, begun in the Jurassic, did not suddenly affect ocean levels. While the Mediterranean was forming during the past 100 million years, the average ocean level was generally 200 metres above current levels. However, the largest known example of marine flooding was when the Atlantic breached the Strait of Gibraltar at the end of the Messinian Salinity Crisis about 5.2 million years ago. This restored Mediterranean sea levels at the sudden end of the period when that basin had dried up, apparently due to geologic forces in the area of the Strait.
Long-term causes Range of effect Vertical effect
Change in volume of ocean basins
Plate tectonics and seafloor spreading (plate divergence/convergence) and change in seafloor elevation (mid-ocean volcanism) Eustatic 0.01 mm/yr
Marine sedimentation Eustatic < 0.01 mm/yr
Change in mass of ocean water
Melting or accumulation of continental ice Eustatic 10 mm/yr
Climate changes during the 20th century
•• Antarctica Eustatic 0.39 to 0.79 mm/yr[12]
•• Greenland (from changes in both precipitation and runoff) Eustatic 0.0 to 0.1 mm/yr
Long-term adjustment to the end of the last ice age
•• Greenland and Antarctica contribution over 20th century Eustatic 0.0 to 0.5 mm/yr
Release of water from earth's interior Eustatic
Release or accumulation of continental hydrologic reservoirs Eustatic
Uplift or subsidence of Earth's surface (Isostasy)
Thermal-isostasy (temperature/density changes in earth's interior) Local effect
Glacio-isostasy (loading or unloading of ice) Local effect 10 mm/yr
Hydro-isostasy (loading or unloading of water) Local effect
Volcano-isostasy (magmatic extrusions) Local effect
Sediment-isostasy (deposition and erosion of sediments) Local effect < 4 mm/yr
Tectonic uplift/subsidence
Vertical and horizontal motions of crust (in response to fault motions) Local effect 1–3 mm/yr
Sediment compaction
Sediment compression into denser matrix (particularly significant in and near river deltas) Local effect
Loss of interstitial fluids (withdrawal of groundwater or oil) Local effect ≤ 55 mm/yr
Earthquake-induced vibration Local effect
Departure from geoid
Shifts in hydrosphere, aesthenosphere, core-mantle interface Local effect
Shifts in earth's rotation, axis of spin and precession of equinox Eustatic
External gravitational changes Eustatic
Evaporation and precipitation (if due to a long-term pattern) Local effect

Changes through geologic time


Comparison of two sea level reconstructions during the last 500 Ma. The scale of change during the last glacial/interglacial transition is indicated with a black bar. Note that over most of geologic history long-term average sea level has been significantly higher than today.

Sea level change since the end of the last glacial episode. Changes displayed in metres.

Sea level has changed over geologic time. As the graph shows, sea level today is very near the lowest level ever attained (the lowest level occurred at the Permian-Triassic boundary about 250 million years ago).

During the most recent ice age (at its maximum about 20,000 years ago) the world's sea level was about 130 m lower than today, due to the large amount of sea water that had evaporated and been deposited as snow and ice, mostly in the Laurentide ice sheet. Most of this had melted by about 10,000 years ago.

Hundreds of similar glacial cycles have occurred throughout the Earth's history. Geologists who study the positions of coastal sediment deposits through time have noted dozens of similar basinward shifts of shorelines associated with a later recovery. This results in sedimentary cycles which in some cases can be correlated around the world with great confidence. This relatively new branch of geological science linking eustatic sea level to sedimentary deposits is called sequence stratigraphy.

The most up-to-date chronology of sea level change through the Phanerozoic shows the following long term trends:[13]
  • Gradually rising sea level through the Cambrian
  • Relatively stable sea level in the Ordovician, with a large drop associated with the end-Ordovician glaciation
  • Relative stability at the lower level during the Silurian
  • A gradual fall through the Devonian, continuing through the Mississippian to long-term low at the Mississippian/Pennsylvanian boundary
  • A gradual rise until the start of the Permian, followed by a gentle decrease lasting until the Mesozoic.

Recent changes

For at least the last 100 years, sea level has been rising at an average rate of about 1.8 mm (0.1 in) per year.[14] Most of this rise can be attributed to the increase in temperature of the sea and the resulting slight thermal expansion of the upper 500 metres (1,640 feet) of sea water. Additional contributions, as much as one-quarter of the total, come from water sources on land, such as melting snow and glaciers and extraction of groundwater for irrigation and other agricultural and human needs.[15]

Aviation

Using pressure to measure altitude results in two other types of altitude. Distance above true or MSL (mean sea level) is the next best measurement to absolute. Above mean sea level is abbreviated as AMSL. MSL altitude is the distance above where sea level would be if there were no land. If one knows the elevation of terrain, the distance above the ground is calculated by a simple subtraction.
An MSL altitude—called pressure altitude by pilots—is useful for predicting physiological responses in unpressurised aircraft (see hypoxia). It also correlates with engine, propeller and wing performance, which all decrease in thinner air.

Pilots can estimate height above terrain with an altimeter set to a defined barometric pressure. Generally, the pressure used to set the altimeter is the barometric pressure that would exist at MSL in the region being flown over. This pressure is referred to as either QNH or "altimeter" and is transmitted to the pilot by radio from air traffic control (ATC) or an Automatic Terminal Information Service (ATIS). Since the terrain elevation is also referenced to MSL, the pilot can estimate height above ground by subtracting the terrain altitude from the altimeter reading. Aviation charts are divided into boxes and the maximum terrain altitude from MSL in each box is clearly indicated. Once above the transition altitude (see below), the altimeter is set to the international standard atmosphere (ISA) pressure at MSL which is 1013.25 hPa or 29.92 inHg.[16]

Flight level

MSL is useful for aircraft to avoid terrain, but at high enough altitudes, there is no terrain to avoid.
Above that level, pilots are primarily interested in avoiding each other, so they adjust their altimeter to standard temperature and pressure conditions (average sea level pressure and temperature) and disregard actual barometric pressure—until descending below transition level. To distinguish from MSL, such altitudes are called flight levels. Standard terminology is to express flight level as hundreds of feet, so FL 240 is 24,000 feet (7,300 m). Pilots use the international standard pressure setting of 1013.25 hPa (29.92 inHg) when referring to flight levels. The altitude at which aircraft are mandated to set their altimeter to flight levels is called "transition altitude". It varies from country to country. For example in the U.S. it is 18,000 feet, in many European countries it is 3,000 or 5,000 feet.

Thermodynamic equilibrium


From Wikipedia, the free encyclopedia

Thermodynamic equilibrium is an axiomatic concept of classical thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by permeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. In a system in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. Systems in mutual thermodynamic equilibrium are simultaneously mutually in thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, almost or perfectly, exactly balanced microscopic exchanges occur; this is part of the notion of macroscopic equilibrium.

An isolated thermodynamic system in its own state of internal thermodynamic equilibrium has a uniform temperature. If its surroundings impose some unchanging long range force field on it, it may consist of one phase or may exhibit several spatially unchanging internal phases. If its surroundings impose no long range force field on it, then either (1) it is spatially homogeneous, with all intensive properties being uniform; or (2) it has several internal phases, which may exhibit indefinitely persistent continuous spontaneous microscopic or mesoscopic fluctuations.

In non-equilibrium systems, by contrast, there are net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, it is said to be in a metastable equilibrium.

It is an axiom of thermodynamics that when a body of material starts from a non-equilibrium state of non-homogeneity or chemical non-equilibrium, and, by a thermodynamic operation, is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. This axiom is presupposed by the second law of thermodynamics, which restricts what can happen when a system, having reached thermodynamic equilibrium, with a well defined entropy, is subject to a thermodynamic operation.

Overview

Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:
A = U - TS
Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:
G = U - TS + PV
where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.

Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.

Conditions for thermodynamic equilibrium

  • For a completely isolated system, S is maximum at thermodynamic equilibrium.
  • For a system with controlled constant temperature and volume, A is minimum at thermodynamic equilibrium.
  • For a system with controlled constant temperature and pressure, G is minimum at thermodynamic equilibrium.
The various types of equilibriums are achieved as follows:
  • Two systems are in thermal equilibrium when their temperatures are the same.
  • Two systems are in mechanical equilibrium when their pressures are the same.
  • Two systems are in diffusive equilibrium when their chemical potentials are the same.
  • All forces are balanced and there is no significant external driving force.

Relation of exchange equilibrium between systems

Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.[1] When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.

A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.

Thermodynamic state of internal equilibrium of a system

A collection of matter may be entirely isolated from its surroundings. Then if left undisturbed for an indefinitely long time, classical thermodynamics postulates that it reaches a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium.[2][3] Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.

Multiple contact equilibrium

The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world, those of them that are in contact then reach respective contact equilibria with one another.

If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.[4][5][6][7] Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.

A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process.[8] It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings.[9][10] The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.[11]

Otherwise, a thermodynamic operation may directly affect a wall of the system.

It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.

Local and global equilibrium

It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.

If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature breaks down, and the temperature becomes undefined.

It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas need not be in thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.

As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.

Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.[12]

Reservations

Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.

For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!"[13]

J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."[14]

Another author, cited by Callen as giving a "scholarly and rigorous treatment",[15] and cited by Adkins as having written a "classic text",[16] A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10100 years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium."[17]

Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." [18]

According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."[19]

Definitions

The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.

Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments."[20] This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.[21]

Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.

For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.[22]

R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium.[23]

In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilbrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".[24] This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".

Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.[25]

Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..."[26] This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.

A student textbook by F.H. Crawford has a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium."[27]

A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium."[28] Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible."[29] It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.[30]

A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." [18] Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal.[1] This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts.
This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.

M. Zemansky also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".[31]

P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.[32]

J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its "full thermodynamic equilibrium state".[33]

Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field.[34]

J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.[35]

Characteristics of a state of internal thermodynamic equilibrium

Homogeneity in the absence of external forces

A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous.[36] This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some intensive variables. For example, a relatively dense component of a mixture can be concentrated by centrifugation.

Uniform temperature

Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable temperature. According to E.A. Guggenheim, "The most important conception of thermodynamics is temperature."[37] Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface."[36] As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals.
Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.

The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. This is so in all cases, including those of non-uniform external force fields.[38][39][40][41][42][43][44][45][46] In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.[47]

Number of real variables needed for specification

In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria.[4] In the opinion of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."[48] This opinion of Prigogine and Defay is in precise agreement with this postulate of Carathéodory. As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.

If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity.

Stability against small perturbations

As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.

Approach to thermodynamic equilibrium within an isolated system

When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium.[47] Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.[49]

Fluctuations within an isolated system in its own internal thermodynamic equilibrium

In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.

To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics.[50] But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.

It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.

If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see.

If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.

If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.

The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.

Thermal equilibrium

An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are occurring several irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process."[51] This illustrates the importance for thermodynamics of the concept of temperature.
Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.[52]

Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.[53]

Non-equilibrium

A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.[54]Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.

General references

  • Cesare Barbieri (2007) Fundamentals of Astronomy. First Edition (QB43.3.B37 2006) CRC Press ISBN 0-7503-0886-9, ISBN 978-0-7503-0886-1
  • Hans R. Griem (2005) Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics), Cambridge University Press, New York ISBN 0-521-61941-6
  • C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases, Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [1]
  • F. Mandl (1988) Statistical Physics, Second Edition, John Wiley & Sons

Lifelong learning

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Lifelong_learning ...