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.
Entropy inequalities for unbounded spin systems
DAI PRA, PAOLO;
2002
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.
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