Large Deviations and Gallavotti–Cohen Principle for Dissipative PDEs with Rough Noise | Zendy

Vojkan Jakšić | Zendy; Vahagn Nersesyan | Zendy; ClaudeAlain Pillet | Zendy; Armen Shirikyan | Zendy

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Large Deviations and Gallavotti–Cohen Principle for Dissipative PDEs with Rough Noise

Author(s) -

Vojkan Jakšić,

Vahagn Nersesyan,

ClaudeAlain Pillet,

Armen Shirikyan

Publication year - 2015

Publication title -

communications in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.662

H-Index - 152

eISSN - 1432-0916

pISSN - 0010-3616

DOI - 10.1007/s00220-014-2279-3

Subject(s) - dissipative system , rate function , entropy production , degenerate energy levels , mathematics , large deviations theory , nonlinear system , fluctuation theorem , entropy (arrow of time) , dissipation , topological entropy , statistical physics , mathematical analysis , physics , pure mathematics , non equilibrium thermodynamics , quantum mechanics

International audienceWe study a class of dissipative PDE's perturbed by an unbounded kick force. Under some natural assumptions, the restrictions of solutions to integer times form a homogeneous Markov process. Assuming that the noise is rough with respect to the space variables and has a non-degenerate law, we prove that the system in question satisfies a large deviation principle in tau-topology. Under some additional hypotheses, we establish a Gallavotti-Cohen type symmetry for the rate function of an entropy production functional and the strict positivity and finiteness of the mean entropy production in the stationary regime. The latter result is applicable to PDE's with strong nonlinear dissipation

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