Dynamical ensembles equivalence in fluid mechanics

Abstract

Dissipative Euler and Navier Stokes equations are discussed with the aim of proposing several experiments apt to test the equivalence of dynamical ensembles and the chaotic hypothesis.

Details on the claims on the cases of formal validity of the pairing rule are collected in the Erratum inserted before the references. The absebce of pairing does not affect the conjecture of equivalence in the paper

References in corpus (5)

• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Dynamical ensembles in stationary states
• Chaotic hypothesis: Extension of Onsager reciprocity to large fields and the chaotic hypothesis
• Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem
• Ergodicity, ensembles, irreversibility in Boltzmann and beyond

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• Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems
• The Gallavotti-Cohen Fluctuation Theorem for a non-chaotic model
• Fluctuations in 2D reversibly-damped turbulence
• Entropy, irreversibility and cascades in the inertial range of isotropic turbulence
• Heat and Fluctuations from Order to Chaos
• Is it possible to experimentally verify the fluctuation relation? A review of theoretical motivations and numerical evidence
• Phase transition in time-reversible Navier-Stokes equations
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• Nonequilibrium and Fluctuation Relation
• Non equilibrium in statistical and fluid mechanics. Ensembles and their equivalence. Entropy driven intermittency
• Anomalies, absence of local equilibrium and universality in 1-d particles systems
• Response Formulae for $n$-point Correlations in Statistical Mechanical Systems and Application to a Problem of Coarse Graining
• Fluctuations of entropy production in turbulent thermal convection
• Time irreversibility in reversible shell models of turbulence
• Constrained Reversible system for Navier-Stokes Turbulence: evidence for Gallavotti's equivalence conjecture
• Equivalent Ensembles, Turbulence and Fluctuation Theorem
• Viscosity, Reversibillity, Chaotic Hypothesis, Fluctuation Theorem and Lyapunov Pairing
• Non-equilibrium Ensembles for the three-dimensional Navier-Stokes Equations
• Spatiotemporal chaos: the microscopic perspective
• Reversible viscosity and Navier--Stokes fluids