Second Law of Thermodynamics without Einstein Relation

TL;DR

This paper challenges the traditional second law of thermodynamics in non-equilibrium systems, proposing a generalized framework that accounts for active contributions and restores fundamental thermodynamic relations.

Contribution

It introduces a temperature-like variable that generalizes the second law for driven systems violating the Einstein relation.

Findings

The Einstein relation does not hold in active, non-equilibrium systems.

Fluctuation relations like Jarzynski and Crooks theorems are invalid in these cases.

A generalized second law with a new temperature variable is proposed, restoring thermodynamic principles.

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.