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Sunday, September 10, 2023

Information overload

From Wikipedia, the free encyclopedia

Information overload (also known as infobesity, infoxication, information anxiety, and information explosion) is the difficulty in understanding an issue and effectively making decisions when one has too much information (TMI) about that issue, and is generally associated with the excessive quantity of daily information. The term "information overload" was first used as early as 1962 by scholars in management and information studies, including in Bertram Gross' 1964 book, The Managing of Organizations, and was further popularized by Alvin Toffler in his bestselling 1970 book Future Shock. Speier et al. (1999) said that if input exceeds the processing capacity, information overload occurs, which is likely to reduce the quality of the decisions.

In a newer definition, Roetzel (2019) focuses on time and resources aspects. He states that when a decision-maker is given many sets of information, such as complexity, amount, and contradiction, the quality of its decision is decreased because of the individual's limitation of scarce resources to process all the information and optimally make the best decision.

The advent of modern information technology has been a primary driver of information overload on multiple fronts: in quantity produced, ease of dissemination, and breadth of the audience reached. Longstanding technological factors have been further intensified by the rise of social media and the attention economy, which facilitates attention theft. In the age of connective digital technologies, informatics, the Internet culture (or the digital culture), information overload is associated with over-exposure, excessive viewing of information, and input abundance of information and data.

Origin of the term

Even though information overload is linked to digital cultures and technologies, Ann Blair notes that the term itself predates modern technologies, as indications of information overload were apparent when humans began collecting manuscripts, collecting, recording, and preserving information. One of the first social scientists to notice the negative effects of information overload was the sociologist Georg Simmel (1858–1918), who hypothesized that the overload of sensations in the modern urban world caused city dwellers to become jaded and interfered with their ability to react to new situations. The social psychologist Stanley Milgram (1933–1984) later used the concept of information overload to explain bystander behavior.

Psychologists have recognized for many years that humans have a limited capacity to store current information in memory. Psychologist George Armitage Miller was very influential in this regard, proposing that people can process about seven chunks of information at a time. Miller says that under overload conditions, people become confused and are likely to make poorer decisions based on the information they have received as opposed to making informed ones.

A quite early example of the term "information overload" can be found in an article by Jacob Jacoby, Donald Speller and Carol Kohn Berning, who conducted an experiment on 192 housewives which was said to confirm the hypothesis that more information about brands would lead to poorer decision making.

Long before that, the concept was introduced by Diderot, although it was not by the term "information overload":

As long as the centuries continue to unfold, the number of books will grow continually, and one can predict that a time will come when it will be almost as difficult to learn anything from books as from the direct study of the whole universe. It will be almost as convenient to search for some bit of truth concealed in nature as it will be to find it hidden away in an immense multitude of bound volumes.

In the internet age, the term "information overload" has evolved into phrases such as "information glut", "data smog", and "data glut" (Data Smog, Shenk, 1997). In his abstract, Kazi Mostak Gausul Hoq commented that people often experience an "information glut" whenever they struggle with locating information from print, online, or digital sources. What was once a term grounded in cognitive psychology has evolved into a rich metaphor used outside the world of academia.

History

Early history

Information overload has been documented throughout periods where advances in technology have increased a production of information. As early as the 3rd or 4th century BC, people regarded information overload with disapproval. Around this time, in Ecclesiastes 12:12, the passage revealed the writer's comment "of making books there is no end" and in the 1st century AD, Seneca the Elder commented, that "the abundance of books is distraction". In 1255, the Dominican Vincent of Beauvais, also commented on the flood of information: "the multitude of books, the shortness of time and the slipperiness of memory." Similar complaints around the growth of books were also mentioned in China. There were also information enthusiasts. The Library of Alexandria was established around the 3rd century BCE or 1st century Rome, which introduced acts of preserving historical artifacts. Museums and libraries established universal grounds of preserving the past for the future, but much like books, libraries were only granted with limited access.

Renaissance

Renaissance humanists always had a desire to preserve their writings and observations, but were only able to record ancient texts by hand because books were expensive and only the privileged and educated could afford them. Humans experience an overload in information by excessively copying ancient manuscripts and replicating artifacts, creating libraries and museums that have remained in the present. Around 1453 AD, Johannes Gutenberg invented the printing press and this marked another period of information proliferation. As a result of lowering production costs, generation of printed materials ranging from pamphlets, manuscripts to books were made available to the average person.

Following Gutenberg's invention, the introduction of mass printing began in Western Europe. Information overload was often experienced by the affluent, but the circulation of books were becoming rapidly printed and available at a lower cost, allowing the educated to purchase books. Information became recordable, by hand, and could be easily memorized for future storage and accessibility. This era marked a time where inventive methods were established to practice information accumulation. Aside from printing books and passage recording, encyclopedias and alphabetical indexes were introduced, enabling people to save and bookmark information for retrieval. These practices marked both present and future acts of information processing.

Swiss scientist Conrad Gessner commented on the increasing number of libraries and printed books, and was most likely the first academic who discussed the consequences of information overload as he observed how "unmanageable" information came to be after the creation of the printing press.

Blair notes that while scholars were elated with the number of books available to them, they also later experienced fatigue with the amount of excessive information that was readily available and overpopulated them. Scholars complained about the abundance of information for a variety of reasons, such as the diminishing quality of text as printers rushed to print manuscripts and the supply of new information being distracting and difficult to manage. Erasmus, one of the many recognized humanists of the 16th century asked, "Is there anywhere on earth exempt from these swarms of new books?".

18th century

Many grew concerned with the rise of books in Europe, especially in England, France, and Germany. From 1750 to 1800, there was a 150% increase in the production of books. In 1795, German bookseller and publisher Johann Georg Heinzmann said "no nation printed as much as the Germans" and expressed concern about Germans reading ideas and no longer creating original thoughts and ideas.

To combat information overload, scholars developed their own information records for easier and simply archival access and retrieval. Modern Europe compilers used paper and glue to cut specific notes and passages from a book and pasted them to a new sheet for storage. Carl Linnaeus developed paper slips, often called his botanical paper slips, from 1767 to 1773, to record his observations. Blair argues that these botanical paper slips gave birth to the "taxonomical system" that has endured to the present, influencing both the mass inventions of the index card and the library card catalog.

Information Age

In his book, The Information: A History, A Theory, A Flood, published in 2011, author James Gleick notes that engineers began taking note of the concept of information, quickly associated it in a technical sense: information was both quantifiable and measurable. He discusses how information theory was created to first bridge mathematics, engineering, and computing together, creating an information code between the fields. English speakers from Europe often equated "computer science" to "informatique, informatica, and Informatik". This leads to the idea that all information can be saved and stored on computers, even if information experiences entropy. But at the same time, the term information, and its many definitions have changed.

In the second half of the 20th century, advances in computer and information technology led to the creation of the Internet.

In the modern Information Age, information overload is experienced as distracting and unmanageable information such as email spam, email notifications, instant messages, Tweets and Facebook(Meta) updates in the context of the work environment. Social media has resulted in "social information overload", which can occur on sites like Meta (previously Facebook), and technology is changing to serve our social culture.

In today's society, day-to-day activities increasingly involve the technological world where information technology exacerbates the number of interruptions that occur in the work environment. Management may be even more disrupted in their decision making, and may result in more poor decisions. Thus, the PIECES framework mentions information overload as a potential problem in existing information systems.

As the world moves into a new era of globalization, an increasing number of people connect to the internet to conduct their own research and are given the ability to contribute to publicly accessible data. This has elevated the risk for the spread of misinformation.

In a 2018 literature review, Roetzel indicates that information overload can be seen as a virus—spreading through (social) media and news networks.

General causes

In a piece published by Slate, Vaughan Bell argues that "Worries about information overload are as old as information itself" because each generation and century will inevitably experience a significant impact with technology. In the 21st century, Frank Furedi describes how an overload in information is metaphorically expressed as a flood, which is an indication that humanity is being "drowned" by the waves of data coming at it. This includes how the human brain continues to process information whether digitally or not. Information overload can lead to "information anxiety", which is the gap between the information that is understood and the information that it is perceived must be understood. The phenomenon of information overload is connected to the field of information technology (IT). IT corporate management implements training to "improve the productivity of knowledge workers". Ali F. Farhoomand and Don H. Drury note that employees often experience an overload in information whenever they have difficulty absorbing and assimilating the information they receive to efficiently complete a task because they feel burdened, stressed, and overwhelmed.

At New York's Web 2.0 Expo in 2008, Clay Shirky's speech indicated that information overload in the modern age is a consequence of a deeper problem, which he calls "filter failure", where humans continue to overshare information with each other. This is due to the rapid rise of apps and unlimited wireless access. In the modern information age, information overload is experienced as distracting and unmanageable information such as email spam, email notifications, instant messages, Tweets, and Facebook updates in the context of the work environment. Social media has resulted in "social information overload", which can occur on sites like Facebook, and technology is changing to serve our social culture. As people view increasing amounts of information in the form of news stories, e-mails, blog posts, Facebook statuses, Tweets, Tumblr posts and other new sources of information, they become their own editors, gatekeepers, and aggregators of information. Social media platforms create a distraction as users attention spans are challenged once they enter an online platform. One concern in this field is that massive amounts of information can be distracting and negatively impact productivity and decision-making and cognitive control. Another concern is the "contamination" of useful information with information that might not be entirely accurate (information pollution).

The general causes of information overload include:

  • A rapidly increasing rate of new information being produced, also known as journalism of assertion, which is a continuous news culture where there is a premium put on how quickly news can be put out; this leads to a competitive advantage in news reporting, but also affects the quality of the news stories reported.
  • The ease of duplication and transmission of data across the Internet.
  • An increase in the available channels of incoming information (e.g. telephone, e-mail, instant messaging, RSS)
  • Ever-increasing amounts of historical information to view.
  • Contradictions and inaccuracies in available information, which is connected to misinformation.
  • A low signal-to-noise ratio.
  • A lack of a method for comparing and processing different kinds of information.
  • The pieces of information are unrelated or do not have any overall structure to reveal their relationships.

Email

E-mail remains a major source of information overload, as people struggle to keep up with the rate of incoming messages. As well as filtering out unsolicited commercial messages (spam), users also have to contend with the growing use of email attachments in the form of lengthy reports, presentations, and media files.

A December 2007 New York Times blog post described E-mail as "a $650 billion drag on the economy", and the New York Times reported in April 2008 that "e-mail has become the bane of some people's professional lives" due to information overload, yet "none of [the current wave of high-profile Internet startups focused on email] really eliminates the problem of e-mail overload because none helps us prepare replies".

In January 2011, Eve Tahmincioglu, a writer for NBC News, wrote an article titled "It's Time to Deal With That Overflowing Inbox". Compiling statistics with commentary, she reported that there were 294 billion emails sent each day in 2010, up from 50 billion in 2009. Quoted in the article, workplace productivity expert Marsha Egan stated that people need to differentiate between working on e-mail and sorting through it. This meant that rather than responding to every email right away, users should delete unnecessary emails and sort the others into action or reference folders first. Egan then went on to say "We are more wired than ever before, and as a result need to be more mindful of managing email or it will end up managing us."

The Daily Telegraph quoted Nicholas Carr, former executive editor of the Harvard Business Review and the author of The Shallows: What The Internet Is Doing To Our Brains, as saying that email exploits a basic human instinct to search for new information, causing people to become addicted to "mindlessly pressing levers in the hope of receiving a pellet of social or intellectual nourishment". His concern is shared by Eric Schmidt, chief executive of Google, who stated that "instantaneous devices" and the abundance of information people are exposed to through e-mail and other technology-based sources could be having an impact on the thought process, obstructing deep thinking, understanding, impeding the formation of memories and making learning more difficult. This condition of "cognitive overload" results in diminished information retaining ability and failing to connect remembrances to experiences stored in the long-term memory, leaving thoughts "thin and scattered". This is also manifest in the education process.

Web accuracy

In addition to e-mail, the World Wide Web has provided access to billions of pages of information. In many offices, workers are given unrestricted access to the Web, allowing them to manage their own research. The use of search engines helps users to find information quickly. However, information published online may not always be reliable, due to the lack of authority-approval or a compulsory accuracy check before publication. Internet information lacks credibility as the Web's search engines do not have the abilities to filter and manage information and misinformation. This results in people having to cross-check what they read before using it for decision-making, which takes up more time.

Viktor Mayer-Schönberger, author of Delete: The Virtue of Forgetting in the Digital Age, argues that everyone can be a "participant" on the Internet, where they are all senders and receivers of information. On the Internet, trails of information are left behind, allowing other Internet participants to share and exchange information. Information becomes difficult to control on the Internet.

The BBC reports that "every day, the information we send and receive online – whether that's checking emails or searching the internet – amount to over 2.5 quintillion bytes of data."

Social media

Social media are applications and websites with an online community where users create and share content with each other, and it adds to the problem of information overload because so many people have access to it. It presents many different views and outlooks on subject matters so that one may have difficulty taking it all in and drawing a clear conclusion. Information overload may not be the core reason for people's anxieties about the amount of information they receive in their daily lives. Instead, information overload can be considered situational. Social media users tend to feel less overloaded by information when using their personal profiles, rather than when their work institutions expect individuals to gather a mass of information. Most people see information through social media in their lives as an aid to help manage their day-to-day activities and not an overload. Depending on what social media platform is being used, it may be easier or harder to stay up to date on posts from people. Facebook users who post and read more than others tend to be able to keep up. On the other hand, Twitter users who post and read a lot of tweets still feel like it is too much information (or none of it is interesting enough). Another problem with social media is that many people create a living by creating content for either their own or someone else's platform, which can create for creators to publish an overload of content.

Effects of information overload

In the context of searching for information, researchers have identified two forms of information overload: outcome overload where there are too many sources of information and textual overload where the individual sources are too long. This form of information overload may cause searchers to be less systematic. Disillusionment when a search is more challenging than expected may result in an individual being less able to search effectively. Information overload when searching can result in a satisficing strategy.

Responding to information overload

Savolainen identifies filtering and withdrawal as common responses to information. Filtering involves quickly working out whether a particular piece of information, such as an email, can be ignored based on certain criteria. Withdrawal refers to limiting the number of sources of information with which one interacts. They distinguish between "pull" and "push" sources of information, a "pull" source being one where one seeks out relevant information, a "push" source one where others decide what information might be interesting. They note that "pull" sources can avoid information overload but by only "pulling" information one risks missing important information.

There have been many solutions proposed for how to mitigate information overload. Research examining how people seek to control an overloaded environment has shown that people purposefully using different coping strategies. In general, overload coping strategy consists of two excluding (ignoring and filtering) and two including (customizing and saving) approaches. Excluding approach focuses on managing the quantity of information, while including approach is geared towards complexity management.

  1. Excluding approach involve the acts of reducing the amount of incoming information. This strategy aims to reduce cognitive burden by decreasing the quantity of information to process through filtering or ignoring. Ignoring is an implicit method, while filtering is explicit, with the main difference being the presence of exposure. Various strategies of excluding, such as reducing the number or volume of information sources and filtering news based on relevance have been described.  Research shows that people are more likely to adopt excluding strategy when they feel overloaded.
  2. Including approach, on the other hand, is a proactive approach where individuals select relevant and important news for consumption, so that one does not miss essential information while preventing excessive energy. Customization and prioritizing are several examples of this type of strategy. Customization, a concept originating from marketing, is one way to organize news based on user preferences. This approach enhances the ability to process information – related to information processing where how a person records, molds, and stores information is crucial. Another inclusion approach is saving. People save or bookmark online content that they come across to read later when they have more time. This strategy does not limit the amount of information acquired but instead focuses on allocating the necessary resources for information processing.

Johnson advises discipline which helps mitigate interruptions and for the elimination of push or notifications. He explains that notifications pull people's attentions away from their work and into social networks and e-mails. He also advises that people stop using their iPhones as alarm clocks which means that the phone is the first thing that people will see when they wake up leading to people checking their e-mail right away.

Clay Shirky states:

What we're dealing with now is not the problem of information overload, because we're always dealing (and always have been dealing) with information overload... Thinking about information overload isn't accurately describing the problem; thinking about filter failure is.

Consider the use of Internet applications and add-ons such as the Inbox Pause add-on for Gmail. This add-on does not reduce the number of e-mails that people get but it pauses the inbox. Burkeman in his article talks about the feeling of being in control is the way to deal with information overload which might involve self-deception. He advises to fight irrationality with irrationality by using add-ons that allow you to pause your inbox or produce other results. Reducing large amounts of information is key.

Dealing with IO from a social network site such as Facebook, a study done by Humboldt University showed some strategies that students take to try and alleviate IO while using Facebook. Some of these strategies included: Prioritizing updates from friends who were physically farther away in other countries, hiding updates from less-prioritized friends, deleting people from their friends list, narrowing the amount of personal information shared, and deactivating the Facebook account.

Illustration for an article published in Diario Uno [es]

The problem of organization

Decision makers performing complex tasks have little if any excess cognitive capacity. Narrowing one's attention as a result of the interruption is likely to result in the loss of information cues, some of which may be relevant to completing the task. Under these circumstances, performance is likely to deteriorate. As the number or intensity of the distractions/interruptions increases, the decision maker's cognitive capacity is exceeded, and performance deteriorates more severely. In addition to reducing the number of possible cues attended to, more severe distractions/interruptions may encourage decision-makers to use heuristics, take shortcuts, or opt for a satisficing decision, resulting in lower decision accuracy.

Some cognitive scientists and graphic designers have emphasized the distinction between raw information and information in a form that can be used in thinking. In this view, information overload may be better viewed as organization underload. That is, they suggest that the problem is not so much the volume of information but the fact that it cannot be discerned how to use it well in the raw or biased form it is presented. Authors who have taken this view include graphic artist and architect Richard Saul Wurman and statistician and cognitive scientist Edward Tufte. Wurman uses the term "information anxiety" to describe humanity's attitude toward the volume of information in general and their limitations in processing it. Tufte primarily focuses on quantitative information and explores ways to organize large complex datasets visually to facilitate clear thinking. Tufte's writing is important in such fields as information design and visual literacy, which deal with the visual communication of information. Tufte coined the term "chartjunk" to refer to useless, non-informative, or information-obscuring elements of quantitative information displays, such as the use of graphics to overemphasize the importance of certain pieces of data or information.

Responding to Information Overload in email communication

In a study conducted by Soucek and Moser (2010), they investigated what impact a training intervention on how to cope with information overload would have on employees. They found that the training intervention did have a positive impact on IO, especially on those who struggled with work impairment and media usage, and employees who had a higher amount of incoming emails.

Responses of business and government

Recent research suggests that an "attention economy" of sorts will naturally emerge from information overload, allowing Internet users greater control over their online experience with particular regard to communication mediums such as e-mail and instant messaging. This could involve some sort of cost being attached to e-mail messages. For example, managers charging a small fee for every e-mail received – e.g. $1.00 – which the sender must pay from their budget. The aim of such charging is to force the sender to consider the necessity of the interruption. However, such a suggestion undermines the entire basis of the popularity of e-mail, namely that e-mails are free of charge to send.

Economics often assumes that people are rational in that they have the knowledge of their preferences and an ability to look for the best possible ways to maximize their preferences. People are seen as selfish and focus on what pleases them. Looking at various parts on their own results in the negligence of the other parts that work alongside it that create the effect of IO. Lincoln suggests possible ways to look at IO in a more holistic approach by recognizing the many possible factors that play a role in IO and how they work together to achieve IO.

In medicine

It would be impossible for an individual to read all the academic papers published in a narrow speciality, even if they spent all their time reading. A response to this is the publishing of systematic reviews such as the Cochrane Reviews. Richard Smith argues that it would be impossible for a general practitioner to read all the literature relevant to every individual patient they consult with and suggests one solution would be an expert system for use of doctors while consulting.

Related terms

Transuranium element

From Wikipedia, the free encyclopedia

The transuranium elements (also known as transuranic elements) are the chemical elements with atomic numbers greater than 92, which is the atomic number of uranium. All of them are radioactively unstable and decay into other elements. With the exception of neptunium and plutonium which have been found in trace amounts in nature, none occur naturally on Earth and they are synthetic.

Overview

Periodic table with elements colored according to the half-life of their most stable isotope.
  Elements which contain at least one stable isotope.
  Slightly radioactive elements: the most stable isotope is very long-lived, with a half-life of over two million years.
  Significantly radioactive elements: the most stable isotope has half-life between 800 and 34,000 years.
  Radioactive elements: the most stable isotope has half-life between one day and 130 years.
  Highly radioactive elements: the most stable isotope has half-life between several minutes and one day.
  Extremely radioactive elements: the most stable known isotope has half-life less than several minutes.

Of the elements with atomic numbers 1 to 92, most can be found in nature, having stable isotopes (such as hydrogen) or very long-lived radioisotopes (such as uranium), or existing as common decay products of the decay of uranium and thorium (such as radon). The exceptions are elements 43, 61, 85, and 87; all four occur in nature, but only in very minor branches of the uranium and thorium decay chains, and thus all save element 87 were first discovered by synthesis in the laboratory rather than in nature (and even element 87 was discovered from purified samples of its parent, not directly from nature).

All the elements with higher atomic numbers have been first discovered in the laboratory, with neptunium and plutonium later also discovered in nature. They are all radioactive, with a half-life much shorter than the age of the Earth, so any primordial atoms of these elements, if they ever were present at the Earth's formation, have long since decayed. Trace amounts of neptunium and plutonium form in some uranium-rich rock, and small amounts are produced during atmospheric tests of nuclear weapons. These two elements are generated from neutron capture in uranium ore with subsequent beta decays (e.g. 238U + n239U239Np239Pu).

All elements heavier than plutonium are entirely synthetic; they are created in nuclear reactors or particle accelerators. The half lives of these elements show a general trend of decreasing as atomic numbers increase. There are exceptions, however, including several isotopes of curium and dubnium. Some heavier elements in this series, around atomic numbers 110–114, are thought to break the trend and demonstrate increased nuclear stability, comprising the theoretical island of stability.

Heavy transuranic elements are difficult and expensive to produce, and their prices increase rapidly with atomic number. As of 2008, the cost of weapons-grade plutonium was around $4,000/gram, and californium exceeded $60,000,000/gram. Einsteinium is the heaviest element that has been produced in macroscopic quantities.

Transuranic elements that have not been discovered, or have been discovered but are not yet officially named, use IUPAC's systematic element names. The naming of transuranic elements may be a source of controversy.

Discovery and naming of transuranium elements

So far, essentially all the transuranium elements have been discovered at four laboratories: Lawrence Berkeley National Laboratory in the United States (elements 93–101, 106, and joint credit for 103–105), the Joint Institute for Nuclear Research in Russia (elements 102 and 114–118, and joint credit for 103–105), the GSI Helmholtz Centre for Heavy Ion Research in Germany (elements 107–112), and RIKEN in Japan (element 113).

Superheavy elements

Position of the transactinide elements in the periodic table.

Superheavy elements, (also known as superheavy atoms, commonly abbreviated SHE) usually refer to the transactinide elements beginning with rutherfordium (atomic number 104). They have only been made artificially, and currently serve no practical purpose because their short half-lives cause them to decay after a very short time, ranging from a few minutes to just a few milliseconds (except for dubnium, which has a half life of over a day), which also makes them extremely hard to study.

Superheavy atoms have all been created since the latter half of the 20th century, and are continually being created during the 21st century as technology advances. They are created through the bombardment of elements in a particle accelerator. For example, the nuclear fusion of californium-249 and carbon-12 creates rutherfordium-261. These elements are created in quantities on the atomic scale and no method of mass creation has been found.

Applications

Transuranium elements may be used to synthesize other superheavy elements. Elements of the island of stability have potentially important military applications, including the development of compact nuclear weapons. The potential everyday applications are vast; the element americium is used in devices such as smoke detectors and spectrometers.

Maximum entropy thermodynamics

In physics, maximum entropy thermodynamics (colloquially, MaxEnt thermodynamics) views equilibrium thermodynamics and statistical mechanics as inference processes. More specifically, MaxEnt applies inference techniques rooted in Shannon information theory, Bayesian probability, and the principle of maximum entropy. These techniques are relevant to any situation requiring prediction from incomplete or insufficient data (e.g., image reconstruction, signal processing, spectral analysis, and inverse problems). MaxEnt thermodynamics began with two papers by Edwin T. Jaynes published in the 1957 Physical Review.

Maximum Shannon entropy

Central to the MaxEnt thesis is the principle of maximum entropy. It demands as given some partly specified model and some specified data related to the model. It selects a preferred probability distribution to represent the model. The given data state "testable information" about the probability distribution, for example particular expectation values, but are not in themselves sufficient to uniquely determine it. The principle states that one should prefer the distribution which maximizes the Shannon information entropy,

This is known as the Gibbs algorithm, having been introduced by J. Willard Gibbs in 1878, to set up statistical ensembles to predict the properties of thermodynamic systems at equilibrium. It is the cornerstone of the statistical mechanical analysis of the thermodynamic properties of equilibrium systems (see partition function).

A direct connection is thus made between the equilibrium thermodynamic entropy STh, a state function of pressure, volume, temperature, etc., and the information entropy for the predicted distribution with maximum uncertainty conditioned only on the expectation values of those variables:

kB, the Boltzmann constant, has no fundamental physical significance here, but is necessary to retain consistency with the previous historical definition of entropy by Clausius (1865) (see Boltzmann constant).

However, the MaxEnt school argue that the MaxEnt approach is a general technique of statistical inference, with applications far beyond this. It can therefore also be used to predict a distribution for "trajectories" Γ "over a period of time" by maximising:

This "information entropy" does not necessarily have a simple correspondence with thermodynamic entropy. But it can be used to predict features of nonequilibrium thermodynamic systems as they evolve over time.

For non-equilibrium scenarios, in an approximation that assumes local thermodynamic equilibrium, with the maximum entropy approach, the Onsager reciprocal relations and the Green–Kubo relations fall out directly. The approach also creates a theoretical framework for the study of some very special cases of far-from-equilibrium scenarios, making the derivation of the entropy production fluctuation theorem straightforward. For non-equilibrium processes, as is so for macroscopic descriptions, a general definition of entropy for microscopic statistical mechanical accounts is also lacking.

Technical note: For the reasons discussed in the article differential entropy, the simple definition of Shannon entropy ceases to be directly applicable for random variables with continuous probability distribution functions. Instead the appropriate quantity to maximize is the "relative information entropy",

Hc is the negative of the Kullback–Leibler divergence, or discrimination information, of m(x) from p(x), where m(x) is a prior invariant measure for the variable(s). The relative entropy Hc is always less than zero, and can be thought of as (the negative of) the number of bits of uncertainty lost by fixing on p(x) rather than m(x). Unlike the Shannon entropy, the relative entropy Hc has the advantage of remaining finite and well-defined for continuous x, and invariant under 1-to-1 coordinate transformations. The two expressions coincide for discrete probability distributions, if one can make the assumption that m(xi) is uniform – i.e. the principle of equal a-priori probability, which underlies statistical thermodynamics.

Philosophical implications

Adherents to the MaxEnt viewpoint take a clear position on some of the conceptual/philosophical questions in thermodynamics. This position is sketched below.

The nature of the probabilities in statistical mechanics

Jaynes (1985, 2003, et passim) discussed the concept of probability. According to the MaxEnt viewpoint, the probabilities in statistical mechanics are determined jointly by two factors: by respectively specified particular models for the underlying state space (e.g. Liouvillian phase space); and by respectively specified particular partial descriptions of the system (the macroscopic description of the system used to constrain the MaxEnt probability assignment). The probabilities are objective in the sense that, given these inputs, a uniquely defined probability distribution will result, the same for every rational investigator, independent of the subjectivity or arbitrary opinion of particular persons. The probabilities are epistemic in the sense that they are defined in terms of specified data and derived from those data by definite and objective rules of inference, the same for every rational investigator. Here the word epistemic, which refers to objective and impersonal scientific knowledge, the same for every rational investigator, is used in the sense that contrasts it with opiniative, which refers to the subjective or arbitrary beliefs of particular persons; this contrast was used by Plato and Aristotle, and stands reliable today.

Jaynes also used the word 'subjective' in this context because others have used it in this context. He accepted that in a sense, a state of knowledge has a subjective aspect, simply because it refers to thought, which is a mental process. But he emphasized that the principle of maximum entropy refers only to thought which is rational and objective, independent of the personality of the thinker. In general, from a philosophical viewpoint, the words 'subjective' and 'objective' are not contradictory; often an entity has both subjective and objective aspects. Jaynes explicitly rejected the criticism of some writers that, just because one can say that thought has a subjective aspect, thought is automatically non-objective. He explicitly rejected subjectivity as a basis for scientific reasoning, the epistemology of science; he required that scientific reasoning have a fully and strictly objective basis. Nevertheless, critics continue to attack Jaynes, alleging that his ideas are "subjective". One writer even goes so far as to label Jaynes' approach as "ultrasubjectivist", and to mention "the panic that the term subjectivism created amongst physicists".

The probabilities represent both the degree of knowledge and lack of information in the data and the model used in the analyst's macroscopic description of the system, and also what those data say about the nature of the underlying reality.

The fitness of the probabilities depends on whether the constraints of the specified macroscopic model are a sufficiently accurate and/or complete description of the system to capture all of the experimentally reproducible behavior. This cannot be guaranteed, a priori. For this reason MaxEnt proponents also call the method predictive statistical mechanics. The predictions can fail. But if they do, this is informative, because it signals the presence of new constraints needed to capture reproducible behavior in the system, which had not been taken into account.

Is entropy "real"?

The thermodynamic entropy (at equilibrium) is a function of the state variables of the model description. It is therefore as "real" as the other variables in the model description. If the model constraints in the probability assignment are a "good" description, containing all the information needed to predict reproducible experimental results, then that includes all of the results one could predict using the formulae involving entropy from classical thermodynamics. To that extent, the MaxEnt STh is as "real" as the entropy in classical thermodynamics.

Of course, in reality there is only one real state of the system. The entropy is not a direct function of that state. It is a function of the real state only through the (subjectively chosen) macroscopic model description.

Is ergodic theory relevant?

The Gibbsian ensemble idealizes the notion of repeating an experiment again and again on different systems, not again and again on the same system. So long-term time averages and the ergodic hypothesis, despite the intense interest in them in the first part of the twentieth century, strictly speaking are not relevant to the probability assignment for the state one might find the system in.

However, this changes if there is additional knowledge that the system is being prepared in a particular way some time before the measurement. One must then consider whether this gives further information which is still relevant at the time of measurement. The question of how 'rapidly mixing' different properties of the system are then becomes very much of interest. Information about some degrees of freedom of the combined system may become unusable very quickly; information about other properties of the system may go on being relevant for a considerable time.

If nothing else, the medium and long-run time correlation properties of the system are interesting subjects for experimentation in themselves. Failure to accurately predict them is a good indicator that relevant macroscopically determinable physics may be missing from the model.

The second law

According to Liouville's theorem for Hamiltonian dynamics, the hyper-volume of a cloud of points in phase space remains constant as the system evolves. Therefore, the information entropy must also remain constant, if we condition on the original information, and then follow each of those microstates forward in time:

However, as time evolves, that initial information we had becomes less directly accessible. Instead of being easily summarizable in the macroscopic description of the system, it increasingly relates to very subtle correlations between the positions and momenta of individual molecules. (Compare to Boltzmann's H-theorem.) Equivalently, it means that the probability distribution for the whole system, in 6N-dimensional phase space, becomes increasingly irregular, spreading out into long thin fingers rather than the initial tightly defined volume of possibilities.

Classical thermodynamics is built on the assumption that entropy is a state function of the macroscopic variables—i.e., that none of the history of the system matters, so that it can all be ignored.

The extended, wispy, evolved probability distribution, which still has the initial Shannon entropy STh(1), should reproduce the expectation values of the observed macroscopic variables at time t2. However it will no longer necessarily be a maximum entropy distribution for that new macroscopic description. On the other hand, the new thermodynamic entropy STh(2) assuredly will measure the maximum entropy distribution, by construction. Therefore, we expect:

At an abstract level, this result implies that some of the information we originally had about the system has become "no longer useful" at a macroscopic level. At the level of the 6N-dimensional probability distribution, this result represents coarse graining—i.e., information loss by smoothing out very fine-scale detail.

Caveats with the argument

Some caveats should be considered with the above.

1. Like all statistical mechanical results according to the MaxEnt school, this increase in thermodynamic entropy is only a prediction. It assumes in particular that the initial macroscopic description contains all of the information relevant to predicting the later macroscopic state. This may not be the case, for example if the initial description fails to reflect some aspect of the preparation of the system which later becomes relevant. In that case the "failure" of a MaxEnt prediction tells us that there is something more which is relevant that we may have overlooked in the physics of the system.

It is also sometimes suggested that quantum measurement, especially in the decoherence interpretation, may give an apparently unexpected reduction in entropy per this argument, as it appears to involve macroscopic information becoming available which was previously inaccessible. (However, the entropy accounting of quantum measurement is tricky, because to get full decoherence one may be assuming an infinite environment, with an infinite entropy).

2. The argument so far has glossed over the question of fluctuations. It has also implicitly assumed that the uncertainty predicted at time t1 for the variables at time t2 will be much smaller than the measurement error. But if the measurements do meaningfully update our knowledge of the system, our uncertainty as to its state is reduced, giving a new SI(2) which is less than SI(1). (Note that if we allow ourselves the abilities of Laplace's demon, the consequences of this new information can also be mapped backwards, so our uncertainty about the dynamical state at time t1 is now also reduced from SI(1) to SI(2)).

We know that STh(2) > SI(2); but we can now no longer be certain that it is greater than STh(1) = SI(1). This then leaves open the possibility for fluctuations in STh. The thermodynamic entropy may go "down" as well as up. A more sophisticated analysis is given by the entropy Fluctuation Theorem, which can be established as a consequence of the time-dependent MaxEnt picture.

3. As just indicated, the MaxEnt inference runs equally well in reverse. So given a particular final state, we can ask, what can we "retrodict" to improve our knowledge about earlier states? However the Second Law argument above also runs in reverse: given macroscopic information at time t2, we should expect it too to become less useful. The two procedures are time-symmetric. But now the information will become less and less useful at earlier and earlier times. (Compare with Loschmidt's paradox.) The MaxEnt inference would predict that the most probable origin of a currently low-entropy state would be as a spontaneous fluctuation from an earlier high entropy state. But this conflicts with what we know to have happened, namely that entropy has been increasing steadily, even back in the past.

The MaxEnt proponents' response to this would be that such a systematic failing in the prediction of a MaxEnt inference is a "good" thing. It means that there is thus clear evidence that some important physical information has been missed in the specification the problem. If it is correct that the dynamics "are" time-symmetric, it appears that we need to put in by hand a prior probability that initial configurations with a low thermodynamic entropy are more likely than initial configurations with a high thermodynamic entropy. This cannot be explained by the immediate dynamics. Quite possibly, it arises as a reflection of the evident time-asymmetric evolution of the universe on a cosmological scale (see arrow of time).

Criticisms

The Maximum Entropy thermodynamics has some important opposition, in part because of the relative paucity of published results from the MaxEnt school, especially with regard to new testable predictions far-from-equilibrium.

The theory has also been criticized in the grounds of internal consistency. For instance, Radu Balescu provides a strong criticism of the MaxEnt School and of Jaynes' work. Balescu states that Jaynes' and coworkers theory is based on a non-transitive evolution law that produces ambiguous results. Although some difficulties of the theory can be cured, the theory "lacks a solid foundation" and "has not led to any new concrete result".

Though the maximum entropy approach is based directly on informational entropy, it is applicable to physics only when there is a clear physical definition of entropy. There is no clear unique general physical definition of entropy for non-equilibrium systems, which are general physical systems considered during a process rather than thermodynamic systems in their own internal states of thermodynamic equilibrium. It follows that the maximum entropy approach will not be applicable to non-equilibrium systems until there is found a clear physical definition of entropy. This problem is related to the fact that heat may be transferred from a hotter to a colder physical system even when local thermodynamic equilibrium does not hold so that neither system has a well defined temperature. Classical entropy is defined for a system in its own internal state of thermodynamic equilibrium, which is defined by state variables, with no non-zero fluxes, so that flux variables do not appear as state variables. But for a strongly non-equilibrium system, during a process, the state variables must include non-zero flux variables. Classical physical definitions of entropy do not cover this case, especially when the fluxes are large enough to destroy local thermodynamic equilibrium. In other words, for entropy for non-equilibrium systems in general, the definition will need at least to involve specification of the process including non-zero fluxes, beyond the classical static thermodynamic state variables. The 'entropy' that is maximized needs to be defined suitably for the problem at hand. If an inappropriate 'entropy' is maximized, a wrong result is likely. In principle, maximum entropy thermodynamics does not refer narrowly and only to classical thermodynamic entropy. It is about informational entropy applied to physics, explicitly depending on the data used to formulate the problem at hand. According to Attard, for physical problems analyzed by strongly non-equilibrium thermodynamics, several physically distinct kinds of entropy need to be considered, including what he calls second entropy. Attard writes: "Maximizing the second entropy over the microstates in the given initial macrostate gives the most likely target macrostate.". The physically defined second entropy can also be considered from an informational viewpoint.

Inequality (mathematics)

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