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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) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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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