Non-equilibrium entropy on stationary Markov processes
type: Item
instance of: scholarly article
title: Non-equilibrium entropy on stationary Markov processes
zbMATH Open document ID: 0569.60066
DOI: 10.1007/BF00047329
author: A. Servet Martínez
published in: Acta Applicandae Mathematicae
publication date: 1985-01-01T00:00:00Z
review text: We study the evolution of probability measures under the action of stationary Markov processes by means of a non-equilibrium entropy defined in terms of a convex function \(\phi\). We prove that the convergence of the non-equilibrium entropy to zero for all measures of finite entropy is independent of \(\phi\) for a wide class of convex functions, including \(\phi_ 0(t)=t \log t.\) We also prove that this is equivalent to the convergence of all the densities of a finite norm to a uniform density, on the Orlicz spaces related to \(\phi\), which include the \(L^ p\)-spaces for \(p>1\). By means of the quadratic function \(\phi_ 2(t)=t^ 2-1\), we relate the nonequilibrium entropies defined by the past \(\sigma\)-algebras of a K- dynamical system with the non-equilibrium entropy of its associated irreversible Markov processes converging to equilibrium.
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 82B05
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 3909470
zbMATH Keywords: evolution of probability measures
zbMATH Keywords: non-equilibrium entropy
zbMATH Keywords: Orlicz spaces
zbMATH Keywords: irreversible Markov processes
MaRDI profile type: Publication
cites work: Q5603641
cites work: Q5644823
cites work: Q5531981
cites work: Q4100724
cites work: Q3931654
cites work: From deterministic dynamics to probabilistic descriptions
cites work: On intrinsic randomness of dynamical systems
cites work: A nonequilibrium entropy for dynamical systems
cites work: Entropy increase in dynamical systems
cites work: Description of a class of Markov processes ''equivalent'' to K-shifts
full work available at URL: https://doi.org/10.1007/bf00047329
OpenAlex ID: W174543469
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description: scientific article; zbMATH DE number 3909470