Viscosity, Reversibillity, Chaotic Hypothesis, Fluctuation Theorem and Lyapunov Pairing

TL;DR

This paper investigates the properties of incompressible fluid equations with UV cut-off, exploring their reversibility, chaotic behavior, and fluctuation relations, and conjectures equivalences with other time-reversible models.

Contribution

It introduces a conjecture linking properties of regularized fluid equations to other time-reversible systems, advancing understanding of chaos and fluctuation theorems in fluid dynamics.

Findings

Properties hold uniformly in the UV cut-off

Conjecture of equivalence with other reversible equations

Analysis of fluctuation relations and Lyapunov pairing

Abstract

Incompressible fluid equations are studied with UV cut-off and in periodic boundary conditions. Properties of the resulting ODEs holding uniformly in the cut-off are considered and, in particular, are conjectured to be equivalent to properties of other time reversible equations. Reversible equations with the same regularization and describing equivalently the fluid, and the fluctuations of large classes of observables, are examined in the context of the "Chaotic Hypothesis", "Axiom C" and the "Fluctuation Theorem".