ISSN:
1572-9036
Keywords:
60J05
;
82A05
;
28D05
;
Markov processes
;
non-equilibrium entropy
;
Orlicz spaces
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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 ϕ. We prove that the convergence of the non-equilibrium entropy to zero for all measures of finite entropy is independent of ϕ for a wide class of convex functions, including ϕ0(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 ϕ, which include the L p -spaces for p〉1. By means of the quadratic function ϕ2(t)=t 2−1, we relate the non-equlibrium entropies defined by the past σ-algebras of a K-dynamical system with the non-equilibrium entropy of its associated irreversible Markov processes converging to equilibrium.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00047329
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