Entropy production and Fluctuation Relation in turbulent thermal convection

Abstract

We report on a numerical experiment performed to analyze fluctuations of the entropy production in turbulent thermal convection, a physical configuration that represents here a prototypical case of an out-of-equilibrium dissipative system. We estimate the entropy production from instantaneous measurements of the local temperature and velocity fields sampled along the trajectory of a large number of point-wise Lagrangian tracers. The entropy production is characterized by large fluctuations and becomes often negative. This represents a sort of "finite-time" violation of the second principle of thermodynamics, since the direction of the energy flux is opposite to that prescribed by the external gradient. We clearly show that the fluctuations of entropy production observed in the present system verify the fluctuation relation (FR), even though the system is time-irreversible.Introduction Fluctuations of physical systems close to equilibrium are well described by the classical linearresponse theory [1][2][3][4], which gives precise predictions on the behavior of the systems and leads to the fluctuationdissipation relations. Current knowledge of the dynamics of systems far away from equilibrium is instead much more limited. The introduction of the so-called fluctuation relation (FR) [5][6][7][8][9] has represented a remarkable result in this area of physics. The FR for nonequilibrium fluctuations reduces to the Green-Kubo and Onsager relations close to equilibrium [10][11][12][13] and represents one of the few exact results for systems kept far from equilibrium. However, a general response-theory for this kind of (nonequilibrium) systems is still to be produced. This suggests that new analyses are required to investigate the behavior of nonequilibrium fluctuations, in particular for macroscopic chaotic systems [14,15].

Probing turbulent superstructures in Rayleigh-Bénard convection by Lagrangian trajectory clusters

“…, v n . In particular, the eigenvector corresponding to the second smallest eigenvalue of (7) approximates the solution of the normalized cut (Ncut) problem introduced by [37] which seeks to minimize the connectivity between clusters while maximizing simultaneously the connectivity within clusters. Eigenvectors corresponding to the next smallest eigenvalues can be used to further subdivide the graph.…”

Constrained Reversible System for Navier-Stokes Turbulence

“…Recently, a model obtained by imposing the constraint that turbulent kinetic energy is conserved has been analysed in 3D turbulence with a small number of modes [81]. Parallel tentatives have been made to test the consequences, namely the fluctuation relations in different systems [4,22,79,89]. Yet, a clear demonstration of the validity of the Gallavotti's conjecture still lacks.…”

Constrained Reversible system for Navier-Stokes Turbulence: evidence for Gallavotti's equivalence conjecture

“…Recently, a model obtained by imposing the constraint that turbulent kinetic energy is conserved has been analysed in 3D turbulence with a small number of modes [64]. Parallel tentatives have been made to test the consequences, namely the fluctuation relations in different systems [2,14,62,70]. While these studies provide motivation to the present work and have given important insights, a clear demonstration of the validity of the Gallavotti's conjecture still lacks.…”