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

TL;DR

This paper explores the validity of the Gallavotti-Cohen Fluctuation Theorem in fluid mechanics using Log-Lattice models, demonstrating its applicability to reversible and, under certain conditions, to traditional Navier-Stokes equations.

Contribution

It introduces a novel approach using Log-Lattices to test the GCFT in fluid dynamics and extends the theorem's applicability to the classical Navier-Stokes equations.

Findings

GCFT holds for the Reversible Navier-Stokes system on Log-Lattices.

The theorem's validity can be extended to traditional Navier-Stokes equations under certain assumptions.

Phase space contraction rate follows a large deviation principle with an estimable rate function.

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.