Entropy Decay for Interacting Systems via the Bochner–bakry–emery Approach
نویسنده
چکیده
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 volumeindependent lower bounds for the Glauber dynamics of interacting point particles and for various classes of hardcore models.
منابع مشابه
Entropy decay for interacting systems via the Bochner – Bakry – Émery approach ∗
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.
متن کاملSpectral gap estimates for interacting particle systems via a Bakry & Emery – type approach
We develop a general technique, based on the Bakry–Emery approach, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In particular, we give a simple and short proof of the diffusive scaling of the spectral gap of the Kawasaki model at high temperature. Similar results are derived for Kawasaki-type dynamics in the lattice wi...
متن کاملOn the Bakry-Emery criterion for linear diffusions and weighted porous media equations
The goal of this paper is to give a non-local sufficient condition for generalized Poincaré inequalities, which extends the well-known Bakry-Emery condition. Such generalized Poincaré inequalities have been introduced by W. Beckner in the gaussian case and provide, along the Ornstein-Uhlenbeck flow, the exponential decay of some generalized entropies which interpolate between the L norm and the...
متن کاملEntropy Dissipation Estimates in a Zero – Range Dynamics
We prove new inequalities implying exponential decay of relative entropy functionals for a class of Zero–Range processes on the complete graph. We first consider the case of uniformly increasing rates, where we use a discrete version of the Bakry– Emery criterium to prove spectral gap and entropy dissipation estimates, uniformly over the number of particles and the number of vertices. We then s...
متن کاملA trajectorial interpretation of the dissipations of entropy and Fisher information for stochastic differential equations
We introduce and develop a pathwise description of the dissipation of general convex entropies for continuous time Markov processes, based on simple backward martingales and convergence theorems with respect to the tail sigma field. The entropy is in this setting the expected value of a backward submartingale. In the case of (non necessarily reversible) Markov diffusion processes, we use Girsan...
متن کامل