Second Law of Thermodynamics without Einstein Relation

Abstract

Materials that are constantly driven out of thermodynamic equilibrium, such as active and living systems, typically violate the Einstein relation. This may arise from active contributions to particle fluctuations which are unrelated to the dissipative resistance of the surrounding medium. We show that in these cases the widely used relation between informatic entropy production and heat dissipation does not hold. Consequently, fluctuation relations for the mechanical work, such as the Jarzynski and Crooks theorems, are invalid. We relate the breaking of the correspondence between entropy production and heat dissipation to departure from the fluctuation-dissipation theorem. We propose a temperaturelike variable that restores this correspondence and gives rise to a generalized second law of thermodynamics, whereby the dissipated heat is necessarily non-negative and vanishes at equilibrium. The Clausius inequality, Carnot maximum efficiency theorem, and relation between the extractable work and the change of free energy are recovered as well.

arXiv comment15 pages

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Cited by in corpus (8)

• Thermodynamics and Statistical Equilibrium of Large-Scale Hydroelastic Wave Turbulence
• Thermodynamic nature of irreversibility in active matter
• Tracer dynamics in an interacting active bath: fluctuations and energy partition
• Probing the limits of effective temperature consistency in actively driven systems
• Inverse Clausius Thermodynamics in Run-and-Tumble Dynamics
• Direct temperature readout in nonequilibrium quantum thermometry
• Matrix approach to generalized ensemble theory for nonequilibrium discrete systems
• Consistent expansion of the Langevin propagator with application to entropy production