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We define a thermostatic system to be a convex space of states together with a concave function sending each state to its entropy, which is an extended real number. This definition applies to classical thermodynamics, classical statistical…

Mathematical Physics · Physics 2023-02-13 John C. Baez , Owen Lynch , Joe Moeller

Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper…

Statistical Mechanics · Physics 2018-10-03 Richard E. Spinney , Joseph T. Lizier , Mikhail Prokopenko

In this document we are interested in entropy. Entropy is multiple, the idea is to describe the definition proposed by the physicist Clausius. Indeed, Clausius exposes in 1865 the second principle of thermodynamics and also proposes the…

Probability · Mathematics 2020-11-11 Ivan Gentil

We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging…

Statistical Mechanics · Physics 2009-11-07 David P. Feldman , James P. Crutchfield

`Entropy' appears as driving force in many different evolution equations, both deterministic and stochastic, and in these equations this `entropy' also takes different forms. We show how all these examples can be understood as different…

Dynamical Systems · Mathematics 2026-03-10 Mark A. Peletier

This is a review of group entropy and its application to permutation complexity. Specifically we revisit a new approach to the notion of complexity in time serie analysis, based on both permutation entropy and group entropy. As a result,…

Mathematical Physics · Physics 2024-01-24 José M. Amigó , Roberto Dale , Piergiulio Tempesta

Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…

Quantum Physics · Physics 2013-05-30 Patrick J. Coles , Roger Colbeck , Li Yu , Michael Zwolak

Shannon's entropy and other entropy-based concepts are derived from the new, more general concept of relative divergence of one "grading' function on a linearly ordered set from another such function. The definition of relative divergence…

Probability · Mathematics 2019-03-14 Alexander Dukhovny

We analyze the nature of the structural order established in liquid TIP4P water in the framework provided by the multi-particle correlation expansion of the statistical entropy. Different regimes are mapped onto the phase diagram of the…

Materials Science · Physics 2011-10-25 Rubens Esposito , Franz Saija , A. Marco Saitta , Paolo V. Giaquinta

With the help of transfer entropy, we analyze information flows between communities of complex networks. We show that the transfer entropy provides a coherent description of interactions between communities, including non-linear…

Statistical Finance · Quantitative Finance 2019-11-18 Jan Korbel , Xiongfei Jiang , Bo Zheng

Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…

Information Theory · Computer Science 2015-03-13 François Bavaud

Multiscale thermodynamics is a theory of relations among levels of description. Energy and entropy are its two main ingredients. Their roles in the time evolution describing approach of a level (starting level) to another level involving…

Statistical Mechanics · Physics 2024-02-26 Miroslav Grmela

'Relativistic thermodynamics' should be understood not as a generalization of a non-relativistic theory but as an application of a general thermodynamic framework, neutral as to spacetime setting and allowing arbitrary conserved quantities,…

Statistical Mechanics · Physics 2025-08-06 David Wallace

Free energy and entropy are examined in detail from the standpoint of classical thermodynamics. The approach is logically based on the fact that thermodynamic work is mediated by thermal energy through the tendency for nonthermal energy to…

Physics Education · Physics 2015-06-26 Clinton D. Stoner

A first principles analysis of an open system thermodynamical Carnot cycle is provided, and the results are compared to those proposed by Gibbs for open systems. The Kelvin-Clausius statement concerning heat transfer for reversible cycles…

General Mathematics · Mathematics 2007-05-23 Christopher G. Jesudason

The formalism used in describing the thermodynamics of abrupt (or first-order) phase transitions is reviewed as an application of maximum entropy inference. In this treatment, we show that the concepts of transition temperature, latent heat…

Statistical Mechanics · Physics 2016-08-01 Sergio Davis , Joaquín Peralta , Yasmín Navarrete , Diego González , Gonzalo Gutiérrez

The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the…

Information Theory · Computer Science 2013-01-29 David Ellerman

The deep connection between entropy and information is discussed in terms of both classical and quantum physics. The mechanism of information transfer between systems via entanglement is explored in the context of decoherence theory. The…

Quantum Physics · Physics 2021-01-05 Martin Paul Vaughan

This paper introduces a framework for modeling cyclical and feedback-driven information flow through a generalized family of entropy-modulated transformations called derangetropy functionals. Unlike scalar and static entropy measures such…

Information Theory · Computer Science 2025-06-17 Masoud Ataei , Xiaogang Wang

We derive a functional for the entropy contributed by any microscopic degrees of freedom as arising from their measurable pair correlations. Applicable both in and out of equilibrium, this functional yields the maximum entropy which a…

Statistical Mechanics · Physics 2023-02-17 Benjamin Sorkin , Joshua Ricouvier , Haim Diamant , Gil Ariel