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- W4315706508 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 $Phi$-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. In this paper,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 $mathbb{R}^n$ to an infinite-dimensionalsetting with weak assumptions on the dynamics." @default.
- W4315706508 created "2023-01-12" @default.
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- W4315706508 date "2023-01-10" @default.
- W4315706508 modified "2023-09-25" @default.
- W4315706508 title "Trajectorial dissipation of $Phi$-entropies for interacting particle systems" @default.
- W4315706508 doi "https://doi.org/10.48550/arxiv.2301.03922" @default.
- W4315706508 hasPublicationYear "2023" @default.
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