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Phase space contraction of degenerately damped random splittings

David P. Herzog and Jonathan C. Mattingly
Vol. 6 (2025), No. 3, 733–775
DOI: 10.2140/pmp.2025.6.733
Abstract

When studying out-of-equilibrium systems, one often excites the dynamics in some degrees of freedom while removing the excitation in others through damping. In order for the system to converge to a statistical steady state, the dynamics must transfer the energy from the excited modes to the dissipative directions. The precise mechanisms underlying this transfer are of particular interest and are the topic of this paper. We explore a class of randomly switched models introduced by Agazzi, Mattingly, and Melikechi (2022; 2023) and provide some of the first results showing that minimal damping is sufficient to stabilize the system in a fluids model.

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Keywords
Lyapunov functions, invariant measures, random splittings, degenerate damping
Mathematical Subject Classification
Primary: 35Q35, 37A50, 60J05
Milestones
Received: 14 April 2024
Revised: 6 January 2025
Accepted: 13 January 2025
Published: 24 March 2025
Authors
David P. Herzog
Department of Mathematics
Iowa State University
Ames, IA
United States
Jonathan C. Mattingly
Department of Mathematics
Duke University
Durham, NC
United States
© 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers).