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Entropy production at weak Gibbs measures and a generalized variational principle

Published online by Cambridge University Press:  01 August 2009

MICHIKO YURI
MICHIKO YURI*
Affiliation:
Department of Mathematics, Graduate School of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810, Japan (email: [email protected])
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Abstract

We consider piecewise invertible systems exhibiting intermittency and establish a generalized variational principle adapted to a non-stationary process in the following sense; the supremum is attained by non-singular (not necessarily invariant) probability measures and if the system exhibits hyperbolicity, then it reduces to the usual variational principle for the pressure. Our method relies on Ruelle’s program in the study of non-equilibrium statistical mechanics to analyze dissipative phenomena. We show non-positivity of entropy production at weak Gibbs measures and clarify when it indeed vanishes. We also discuss a generalized variational principle in the context of σ-finite invariant measures.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 4 , August 2009 , pp. 1327 - 1347
Copyright
Copyright © Cambridge University Press 2009

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