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.
Keywords
Lyapunov functions, invariant measures, random splittings,
degenerate damping
