Numerical investigations around the Gallavotti-Cohen fluctuation theorem on log-lattices

Using the recent concept of fluids projected onto log-lattices (LL), 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 (FT). To address this issue, Gallavotti introduced a new model, the reversible Navier-Stokes (RNS) equations, 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 LL, the GCFT holds for the RNS system. Furthermore, we show that this result can be extended, under certain assumptions, to the traditional, irreversible NS equations. In addition, we show that the phase space contraction rate satisfies a large deviation relation whose rate function can be estimated. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.