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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

We give meaning to the first and second laws of thermodynamics in case of mesoscopic out-of-equilibrium systems which are driven by diffusion processes. The notion of the entropy production is analyzed. The role of the Helmholtz extremum…

Statistical Mechanics · Physics 2008-11-26 Piotr Garbaczewski

This paper is a non-technical, informal presentation of our theory of the second law of thermodynamics as a law that is independent of statistical mechanics and that is derivable solely from certain simple assumptions about adiabatic…

Mathematical Physics · Physics 2009-10-31 Elliott H. Lieb , Jakob Yngvason

This paper describes an entropy equation, but one that should be used for measuring energy and not information. In relation to the human brain therefore, both of these quantities can be used to represent the stored information. The human…

Artificial Intelligence · Computer Science 2020-08-12 Kieran Greer

Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…

Mathematical Physics · Physics 2025-08-26 Hong Qian , Zhongwei Shen

In the sciences in general, the phrase "route to chaos" has come to refer to a metaphor when some physical, biological, economic, or social system transitions from one exhibiting order to one displaying randomness (or chaos). Sometimes the…

Dynamical Systems · Mathematics 2023-02-14 Sylvain Crovisier , Enrique Pujals

Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle…

Statistical Mechanics · Physics 2024-07-11 Benjamin Sorkin , Haim Diamant , Gil Ariel

In this article a definition of reversible processes in terms of differences in intensive Thermodynamics properties (Affinities) is proposed. This definition makes it possible to both define reversible processes before introducing the…

Classical Physics · Physics 2016-08-09 Hernán A. Ritacco

Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue…

Quantum Physics · Physics 2019-05-01 Thomas Dittrich

We introduce an ambidextrous view of stochastic dynamical systems, comparing their forward-time and reverse-time representations and then integrating them into a single time-symmetric representation. The perspective is useful theoretically,…

Statistical Mechanics · Physics 2015-05-13 Christopher J. Ellison , John R. Mahoney , James P. Crutchfield

Natural resource use and waste production, disposal, and reuse in human economies are treated in their economic, technological and thermodynamic aspects. The physical nature of economic production, consumption, saving, and waste is compared…

Condensed Matter · Physics 2008-02-03 Dallas C. Kennedy

Entropic Dynamics is a framework in which dynamical laws such as those that arise in physics are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by…

Quantum Physics · Physics 2018-02-23 Ariel Caticha

We introduce the concepts of closed sets and closure operators as mathematical tools for the study of social networks. Dynamic networks are represented by transformations. It is shown that under continuous change/transformation, all…

Combinatorics · Mathematics 2012-12-13 John L. Pfaltz

In this article we discuss a model used to introduce the concept of entropy with secondary school students. It can be used to discuss with students the reversibility of time, the tendency towards homogeneity and the link between probability…

Physics Education · Physics 2014-09-10 Tommaso Castellani

Non-reciprocal interactions are present in many systems out of equilibrium. The rate of entropy production is a measure that quantifies the time irreversibility of a system, and thus how far it is from equilibrium. In this work, we…

Statistical Mechanics · Physics 2022-11-28 Ziluo Zhang , Rosalba Garcia-Millan

The thermodynamic approach to non-equilibrium dynamics describes the state of macroscopic systems by means of a collection of intensities or intensive variables. The latter are by definition the differentials of the entropy with respect to…

chao-dyn · Physics 2008-02-03 Z. Hens , X. de Hemptinne

Thermodynamics is based on the notions of energy and entropy. While energy is the elementary quantity governing physical dynamics, entropy is the fundamental concept in information theory. In this work, starting from first principles, we…

Statistical Mechanics · Physics 2017-10-25 Bernhard Altaner

The reversibility and recurrence paradoxes are key issues that have been left unsolved in researches on the foundation of thermodynamics since the 19th century. This article shows that (1) the reversibility paradox can be overcome if we pay…

Statistical Mechanics · Physics 2021-07-27 Yoshihiro Nakato

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 chapter concerns "control volume analysis", the standard engineering tool for the analysis of flow systems, and its application to entropy balance calculations. Firstly, the principles of control volume analysis are enunciated and…

Fluid Dynamics · Physics 2014-07-22 Robert K. Niven , Bernd R. Noack
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