Non-equilibrium entropy on stationary Markov processes

✍ Scribed by A. Servet Martínez

• Publisher: Springer Netherlands
• Year: 1985
• Tongue: English
• Weight: 774 KB
• Volume: 3
• Category: Article
• ISSN: 0167-8019
• DOI: 10.1007/bf00047329

✦ Synopsis

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 $. We prove that the convergence of the non-equilibrium entropy to zero for all measures of finite entropy is independent of for a wide class of convex functions, including ~po(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 $, which include the Le-spaces for p > 1. By means of the quadratic function t~2(t ) = t 2 -1, we relate the nonequilibrium entropies defined by the past a-algebras of a K-dynamical system with the non-equilibrium entropy of its associated irreversible Markov processes converging to equilibrium. AMS (MOS) subject classifications (1950). 60J05, 82A05, 28D05.