Entropy Inequalities for Unbounded Spin Systems

We consider nonconservative, reversible spin systems, with unbounded discrete spins. We show that for a class of these dynamics in a high temperature regime, the relative entropy with respect to the equilibrium distribution decays exponentially in time, although the logarithmic-Sobolev inequality fa...

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Veröffentlicht in:	The Annals of probability 2002-10, Vol.30 (4), p.1959-1976
Hauptverfasser:	Pra, Paolo Dai, Paganoni, Anna Maria, Posta, Gustavo
Format:	Artikel
Sprache:	eng
Schlagworte:	60K35 82C22 Boundary conditions Classical ensemble theory Classical statistical mechanics Entropy Exact sciences and technology logarithmic-Sobolev inequality Markov processes Mathematical inequalities Mathematical theorems Mathematics Physics Probabilities Probability and statistics Probability theory and stochastic processes Rectangles Sciences and techniques of general use Semigroups Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) spectral gap Spectroscopic analysis Spin systems Statistical physics, thermodynamics, and nonlinear dynamical systems Thermodynamic equilibrium
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Beschreibung
Zusammenfassung:	We consider nonconservative, reversible spin systems, with unbounded discrete spins. We show that for a class of these dynamics in a high temperature regime, the relative entropy with respect to the equilibrium distribution decays exponentially in time, although the logarithmic-Sobolev inequality fails. To this end we prove a weaker modification of the logarithmic-Sobolev inequality.
ISSN:	0091-1798 2168-894X
DOI:	10.1214/aop/1039548378