Large deviations and entropy production in viscous fluid flows
Abstract
We study the motion of a particle in a random time-dependent vector field defined by the 2D Navier-Stokes system with a noise. Under suitable non-degeneracy hypotheses we prove that the empirical measures of the trajectories of the pair (velocity field, particle) satisfy the LDP with a good rate function. Moreover, we show that the law of a unique stationary solution restricted to the particle component possesses a positive smooth density with respect to the Lebesgue measure in any finite time. This allows one to define a natural concept of the entropy production, and to show that its time average is a bounded function of the trajectory. The proofs are based on a new criterion for the validity of the level-3 LDP for Markov processes and an application of a general result on the image of probability measures under smooth maps to the laws associated with the motion of the particle.
Cite
@article{arxiv.1902.03278,
title = {Large deviations and entropy production in viscous fluid flows},
author = {Vojkan Jaksic and Vahagn Nersesyan and Claude-Alain Pillet and Armen Shirikyan},
journal= {arXiv preprint arXiv:1902.03278},
year = {2019}
}
Comments
52 pages