The Annals of Probability

Entropy inequalities for unbounded spin systems

Paolo Dai Pra, Anna Maria Paganoni, and Gustavo Posta

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Abstract

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.

Article information

Source
Ann. Probab., Volume 30, Number 4 (2002), 1959-1976.

Dates
First available in Project Euclid: 10 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1039548378

Digital Object Identifier
doi:10.1214/aop/1039548378

Mathematical Reviews number (MathSciNet)
MR1944012

Zentralblatt MATH identifier
1013.60076

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35]

Keywords
Spin systems entropy logarithmic-Sobolev inequality spectral gap

Citation

Dai Pra, Paolo; Paganoni, Anna Maria; Posta, Gustavo. Entropy inequalities for unbounded spin systems. Ann. Probab. 30 (2002), no. 4, 1959--1976. doi:10.1214/aop/1039548378. https://projecteuclid.org/euclid.aop/1039548378


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