Open Access
May 2015 Large deviations and the Boltzmann entropy formula
Giovanni Jona-Lasinio
Braz. J. Probab. Stat. 29(2): 494-501 (May 2015). DOI: 10.1214/14-BJPS266

Abstract

In the last decade, the theory of large deviations has become a main tool in statistical mechanics especially in the study of non-equilibrium. In a rational reconstruction of the story, one must recognize the ideal connection and debt of some recent work, to discussions taking place at the beginning of the twentieth century. The famous equation $S=k\ln W$ usually attributed to Boltzmann, actually written in this final form by Planck on his route to the quantum hypothesis, was interpreted by Einstein as a large deviation formula. This interpretation, on which he based his theory of thermodynamic equilibrium fluctuations, has been a source of inspiration in recent developments of non-equilibrium statistical mechanics. In this paper, we briefly illustrate this aspect.

Citation

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Giovanni Jona-Lasinio. "Large deviations and the Boltzmann entropy formula." Braz. J. Probab. Stat. 29 (2) 494 - 501, May 2015. https://doi.org/10.1214/14-BJPS266

Information

Published: May 2015
First available in Project Euclid: 15 April 2015

zbMATH: 1318.82034
MathSciNet: MR3336877
Digital Object Identifier: 10.1214/14-BJPS266

Keywords: Boltzmann formula , large fluctuations , non-equilibrium states

Rights: Copyright © 2015 Brazilian Statistical Association

Vol.29 • No. 2 • May 2015
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