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Open AccessArticle

Thermodynamics Beyond Molecules: Statistical Thermodynamics of Probability Distributions

Department of Chemical Engineering, Pennsylvania State University, University Park, PA 16802, USA
Entropy 2019, 21(9), 890; https://doi.org/10.3390/e21090890
Received: 26 July 2019 / Revised: 5 September 2019 / Accepted: 11 September 2019 / Published: 13 September 2019
(This article belongs to the Section Information Theory, Probability and Statistics)
Statistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, what is thermodynamics, has remained unanswered. We answer this question here. Generalized statistical thermodynamics is a variational calculus of probability distributions. It is independent of physical hypotheses but provides the means to incorporate our knowledge, assumptions and physical models about a stochastic processes that gives rise to the probability in question. We derive the familiar calculus of thermodynamics via a probabilistic argument that makes no reference to physics. At the heart of the theory is a space of distributions and a special functional that assigns probabilities to this space. The maximization of this functional generates the mathematical network of thermodynamic relationship. We obtain statistical mechanics as a special case and make contact with Information Theory and Bayesian inference. View Full-Text
Keywords: statistical thermodynamics; statistical mechanics; biased sampling; most probable distribution statistical thermodynamics; statistical mechanics; biased sampling; most probable distribution
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MDPI and ACS Style

Matsoukas, T. Thermodynamics Beyond Molecules: Statistical Thermodynamics of Probability Distributions. Entropy 2019, 21, 890.

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