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Entropy 2014, 16(6), 3173-3206; doi:10.3390/e16063173

Relative Entropy, Interaction Energy and the Nature of Dissipation

1, 2, 3 and 4,*
1 Laboratoire analyse et physique mathématique, 14 avenue Félix Faure, 75015 Paris, France 2 Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany 3 Université Pierre et Marie Curie, LPTMC, case 121, 4 pl. Jussieu, 75252 Paris cedex 05, France 4 Physics Department, Clarkson University, Potsdam, New York 13699-5820, USA
* Author to whom correspondence should be addressed.
Received: 10 February 2014 / Revised: 20 April 2014 / Accepted: 23 May 2014 / Published: 6 June 2014
(This article belongs to the Special Issue Complex Systems)


Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a. Kullback-Leibler divergence). The processes considered are general time evolutions both in classical and quantum mechanics, and the initial state is sometimes thermal, sometimes partially so. By calculating a transport coefficient we show that indeed—at least in this case—the source of dissipation in that coefficient is the relative entropy.
Keywords: relative entropy; dissipation; thermodynamic inequalities; interaction energy relative entropy; dissipation; thermodynamic inequalities; interaction energy
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Gaveau, B.; Granger, L.; Moreau, M.; Schulman, L.S. Relative Entropy, Interaction Energy and the Nature of Dissipation. Entropy 2014, 16, 3173-3206.

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