Journal of Statistical Physics

, Volume 155, Issue 1, pp 93–105 | Cite as

Gibbs–Jaynes Entropy Versus Relative Entropy

  • M. Meléndez
  • P. Español


The maximum entropy formalism developed by Jaynes determines the relevant ensemble in nonequilibrium statistical mechanics by maximising the entropy functional subject to the constraints imposed by the available information. We present an alternative derivation of the relevant ensemble based on the Kullback–Leibler divergence from equilibrium. If the equilibrium ensemble is already known, then calculation of the relevant ensemble is considerably simplified. The constraints must be chosen with care in order to avoid contradictions between the two alternative derivations. The relative entropy functional measures how much a distribution departs from equilibrium. Therefore, it provides a distinct approach to the calculation of statistical ensembles that might be applicable to situations in which the formalism presented by Jaynes performs poorly (such as non-ergodic dynamical systems).


Gibbs–Jaynes entropy Kullback–Leibler divergence Relative entropy Maximum entropy formalism Nonequilibrium statistical mechanics 



We would like to express our gratitude to the anonymous reviewers of this article for their insightful comments.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Departamento de Física FundamentalUniversidad Nacional de Educación a Distancia MadridSpain

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