Entropy decay for interacting systems via the Bochner--Bakry--Emery approach

TL;DR

This paper extends the Bakry-Emery approach to analyze the exponential decay of relative entropy in Markov processes with non-local generators, providing volume-independent bounds for certain interacting particle systems.

Contribution

It adapts the Bakry-Emery method to non-local generators, deriving new entropy decay estimates for Glauber dynamics and hardcore models.

Findings

Volume-independent entropy decay bounds for Glauber dynamics

Exponential decay estimates for interacting point particles

Application of Bakry-Emery approach to non-local Markov processes

Abstract

We obtain estimates on the exponential rate of decay of the relative entropy from equilibrium for Markov processes with a non-local infinitesimal generator. We adapt some of the ideas coming from the Bakry-Emery approach to this setting. In particular, we obtain volume-independent lower bounds for the Glauber dynamics of interacting point particles and for various classes of hardcore models.