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arXiv · 1902.03278

Large deviations and entropy production in viscous fluid flows

Vojkan Jaksic·Vahagn Nersesyan·Claude-Alain Pillet·Armen Shirikyan
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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.

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Vojkan Jaksic, Vahagn Nersesyan, Claude-Alain Pillet, Armen Shirikyan. 2019-02-08. Large deviations and entropy production in viscous fluid flows. https://arxiv.org/abs/1902.03278

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