Trajectorial Dissipation of Φ-Entropies for Interacting Particle Systems

A classical approach for the analysis of the long-time behaviour of Markov processes is to consider suitable Lyapunov functionals like the variance or more generally Φ -entropies. Via purely analytic arguments it can be shown that these functionals are indeed non-increasing in time under quite gener...

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Bibliographic Details
Published in:Journal of statistical physics 2023-07, Vol.190 (7)
Main Authors: Jahnel, Benedikt, Köppl, Jonas
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary:A classical approach for the analysis of the long-time behaviour of Markov processes is to consider suitable Lyapunov functionals like the variance or more generally Φ -entropies. Via purely analytic arguments it can be shown that these functionals are indeed non-increasing in time under quite general assumptions on the process. We refine these classical results via a more probabilistic approach and show that dissipation is already present on the level of individual trajectories for spatially extended systems of infinitely many interacting particles with arbitrary underlying geometry and compact local spin spaces. This extends previous results from the setting of finite-state Markov chains or diffusions in R n to an infinite-dimensional setting with weak assumptions on the dynamics.
ISSN:1572-9613
DOI:10.1007/s10955-023-03136-0