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Entropy Inequalities for Unbounded Spin Systems
Paolo Dai Pra, Anna Maria Paganoni and Gustavo Posta
The Annals of Probability
Vol. 30, No. 4 (Oct., 2002), pp. 1959-1976
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/1558841
Page Count: 18
You can always find the topics here!Topics: Entropy, Mathematical inequalities, Rectangles, Boundary conditions, Probabilities, Semigroups, Markov processes, Fats, Mathematical theorems, Spectroscopic analysis
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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.
The Annals of Probability © 2002 Institute of Mathematical Statistics