WIAS Preprint No. 3019, (2023)

Trajectorial dissipation of $Phi$-entropies for interacting particle systems


Authors

  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Köppl, Jonas
    ORCID: 0000-0001-9188-1883

2020 Mathematics Subject Classification

  • 82C20 60K35

Keywords

  • Interacting particle systems, phi-entropy, time-reversal, martingale representation

DOI

10.20347/WIAS.PREPRINT.3019

Abstract

A classical approach for the analysis of the longtime behavior 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 complement 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 Rn to an infinite-dimensional setting with weak assumptions on the dynamics.

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