The Hatano-Sasa equality: Transitions between steady states in a granular gas The Hatano-Sasa equality: Transitions between steady states in a granular gas

Anne Mounier (1) , Antoine Naert (1)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

– An experimental study is presented, about transitions between Non-Equilibrium Steady States (NESS) in a dissipative medium. The core device is a small rotating blade that imposes cycles of increasing and decreasing forcings to a granular gas, shaken independently. The velocity of this blade is measured, subject to the transitions imposed by the periodic torque variation. The Hatano-Sasa (HS) equality, that generalises the second principle of thermodynamics to NESS, is verified with a high accuracy (a few 10 −3), at different variation rates. Besides, it is observed that the fluctuating velocity at fixed forcing follows a generalised Gumbel distribution. A rough evaluation of the mean free path in the granular gas suggests that it might be a correlated system, at least partially. Introduction. – Recent decades have seen significant progress in non-equilibrium statistical mechanics, with the advent of the Fluctuation Theorems, the Jarzynski and Crooks relations [1–3]. These relations were at the time theoretical advances, with the support of the numerics. Experimental contributions came later, mostly because of technical limits. Indeed, the scales at which thermal energy dominates are small. Measurements of fluctuations at such scales has been prohibitively difficult until recently. Usually, an inequality involving the average entropy production is the expression of the second principle of thermodynamics. The improvement brought by the fluctuation theorems is that an instantaneous rate of entropy production is expressed by an equality. It is somehow a local formulation. The Jarzynski equality relates the Helmholtz free energy difference ∆F between two states A and B, to the average of the exponentiated work needed to perform the transition: e −β∆F = e −βW

Domaines: Physique [physics]; Mécanique statistique [cond-mat.stat-mech]

Anne Mounier, Antoine Naert. The Hatano-Sasa equality: Transitions between steady states in a granular gas The Hatano-Sasa equality: Transitions between steady states in a granular gas. EPL - Europhysics Letters, 2012, pp.11004. ⟨hal-01141357⟩