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
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container_end_page 1976
container_issue 4
container_start_page 1959
container_title The Annals of probability
container_volume 30
creator Pra, Paolo Dai
Paganoni, Anna Maria
Posta, Gustavo
description 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.
doi_str_mv 10.1214/aop/1039548378
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source Project Euclid; EZB-FREE-00999 freely available EZB journals; JSTOR; JSTOR Mathematics & Statistics Collection
subjects 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
title Entropy Inequalities for Unbounded Spin Systems
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