Modern Thermodynamics, by Arieh Ben-Naim and Diego Casadei (original) (raw)

Entropy: From Thermodynamics to Information Processing

Entropy, 2021

Entropy is a concept that emerged in the 19th century. It used to be associated with heat harnessed by a thermal machine to perform work during the Industrial Revolution. However, there was an unprecedented scientific revolution in the 20th century due to one of its most essential innovations, i.e., the information theory, which also encompasses the concept of entropy. Therefore, the following question is naturally raised: “what is the difference, if any, between concepts of entropy in each field of knowledge?” There are misconceptions, as there have been multiple attempts to conciliate the entropy of thermodynamics with that of information theory. Entropy is most commonly defined as “disorder”, although it is not a good analogy since “order” is a subjective human concept, and “disorder” cannot always be obtained from entropy. Therefore, this paper presents a historical background on the evolution of the term “entropy”, and provides mathematical evidence and logical arguments regard...

Fundamentals of Information Thermodynamics and its Applications

Fundamentals of Information Thermodynamics and its Applications, 2019

The term "Information Thermodynamics" came in use as early as in 1979 and is being used, e.g., in Physical review E (to the author's complete surprise, for he was convinced about his own and autonomous authorship of this term for many years, roughly between 2001 and 2012. The author made an attempt to unify systematically the typical branches, dealing with the (even broader) sense of the term "information" and also with this term itself. His unification of Thermodynamics, Information Theory and the Theory of Computing and Logics together, by the term "structure" and the term "information" just as the measure of the structure (structure - is the distribution of energy in space and time) and especially by the term "information transfer" (which is the measuring/observation of the structure as well as the communication by messages and also the recording of messages), is also called (by him) the Information Thermodynamics. The information-thermodynamic approach seems to be of a great power in a variety of branches.

Information Thermodynamics (Basic Ideas)

Thermodynamic Physical Chemistry of Aqueous Systems, 2011

We apply a certain unifying physical description of the results of Information Theory. Assuming that heat entropy is a thermodynamic realization of information entropy, we construct a cyclical, thermodynamic, average-value model of an information transfer chain as a general heat engine, in particular a Carnot engine, reversible or irreversible. A working medium of the cycle (a thermodynamic system transforming input heat energy) can be considered as a thermodynamic, average-value model or, as such, as a realization of an information transfer channel. We show that for a model realized in this way the extended II. Principle of Thermodynamics is valid and we formulate its \textit{information form. In addition we solve the problem of a proof of II. Principle of Thermodynamics. We state the relation between the term of information entropy, introduced by C. Shannon (1948), and thermodynamic entropy, introduced by R. Clausius (1850) and, further, explain the Gibbs paradox. Our way to deal with the given topic is a connection of both the mathematical definitions of information entropies and their mutual relations within a system of stochastic quantities, especially with thermodynamic entropies defined on an isolated system in which a realization of our (repeatable) observation is performed [it is a (cyclic) transformation of heat energy of an observed, measure} system]. We use the information description to analyze the Gibbs paradox, reasoning it as a property of such observation, measuring an (equilibrium) thermodynamic system. We state a logical proof of the II.~P.T. as a derivation of relations among the entropies of a system of stochastic variables, realized physically, and, the Equivalence Principle of the I., II. and III. Principle of Thermodynamics is formulated.

The use of the information-theoretic entropy in thermodynamics

Studies In History and Philosophy of …

When considering controversial thermodynamic scenarios such as Maxwell's demon, it is often necessary to consider probabilistic mixtures of macrostates. This raises the question of how, if at all, to assign entropy to them. The information-theoretic entropy is often used in such ...

Entropy and Information Theory: Uses and Misuses

Entropy

This article is about the profound misuses, misunderstanding, misinterpretations and misapplications of entropy, the Second Law of Thermodynamics and Information Theory. It is the story of the “Greatest Blunder Ever in the History of Science”. It is not about a single blunder admitted by a single person (e.g., Albert Einstein allegedly said in connection with the cosmological constant, that this was his greatest blunder), but rather a blunder of gargantuan proportions whose claws have permeated all branches of science; from thermodynamics, cosmology, biology, psychology, sociology and much more.

On Entropy, Information, and Conservation of Information

Entropy

The term entropy is used in different meanings in different contexts, sometimes in contradictory ways, resulting in misunderstandings and confusion. The root cause of the problem is the close resemblance of the defining mathematical expressions of entropy in statistical thermodynamics and information in the communications field, also called entropy, differing only by a constant factor with the unit ‘J/K’ in thermodynamics and ‘bits’ in the information theory. The thermodynamic property entropy is closely associated with the physical quantities of thermal energy and temperature, while the entropy used in the communications field is a mathematical abstraction based on probabilities of messages. The terms information and entropy are often used interchangeably in several branches of sciences. This practice gives rise to the phrase conservation of entropy in the sense of conservation of information, which is in contradiction to the fundamental increase of entropy principle in thermodynam...