Numerical investigations around the Gallavotti-Cohen Fluctuation Theorem on Log-lattices

Guillaume Costa; Bérengère Dubrulle

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arXiv · 2508.17943

Numerical investigations around the Gallavotti-Cohen Fluctuation Theorem on Log-lattices

Guillaume Costa·Bérengère Dubrulle

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Abstract

Using the recent concept of fluids projected onto Log-Lattices, we investigate the validity of the Gallavotti-Cohen Fluctuation Theorem (GCFT) in the context of fluid mechanics. The dynamics of viscous flows are inherently irreversible, which violates a fundamental assumption of the fluctuation theorem. To address this issue, Gallavotti introduced a new model, the Reversible Navier-Stokes Equation (RNS), which recovers the time-reversal symmetry of the Navier-Stokes (NS) equations while retaining the core characteristics of the latter. We show that for fluids on Log-Lattices, the GCFT holds for the RNS system. Furthermore, we show that this result can be extended, under certain assumptions, to the traditional, irreversible Navier-Stokes equations. Additionally, we show that the phase space contraction rate satisfies a large deviation relation which rate function can be estimated.

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Guillaume Costa, Bérengère Dubrulle. 2025-08-25. Numerical investigations around the Gallavotti-Cohen Fluctuation Theorem on Log-lattices. https://arxiv.org/abs/2508.17943

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