标题： 围绕对数格点上的Gallavotti-Cohen涨落定理的数值研究 显示英文标题

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

摘要： 使用流体投影到对数格子的最新概念，我们研究了在流体力学背景下Gallavotti-Cohen涨落定理（GCFT）的有效性。粘性流动的动力学本质上是不可逆的，这违背了涨落定理的一个基本假设。为了解决这个问题，Gallavotti引入了一个新模型，即可逆的Navier-Stokes方程（RNS），该模型在保留Navier-Stokes（NS）方程核心特性的同时恢复了Navier-Stokes方程的时间反演对称性。我们证明对于对数格子上的流体，GCFT适用于RNS系统。此外，我们证明在某些假设下，这一结果可以扩展到传统的不可逆Navier-Stokes方程。此外，我们证明相空间收缩率满足一个大偏差关系，其速率函数可以估计。 显示英文摘要

摘要： 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.