Inequalities generalizing the second law of thermodynamics for transitions between non-stationary states

TL;DR

This paper extends the second law of thermodynamics to non-stationary states using a variant of the Hatano-Sasa relation, introducing new inequalities and connecting non-stationary distributions to traffic differences in dynamics.

Contribution

It generalizes the Hatano-Sasa relation for non-stationary states and introduces inequalities that extend thermodynamic principles beyond stationary conditions.

Findings

Derived a relation linking non-stationary distributions to traffic differences.

Extended the definitions of adiabatic and non-adiabatic entropies for non-stationary states.

Established second-law like inequalities for transitions between non-stationary states.

Abstract

We discuss the consequences of a variant of the Hatano-Sasa relation in which a non-stationary distribution is used in place of the usual stationary one. We first show that this non-stationary distribution is related to a difference of traffic between the direct and dual dynamics. With this formalism, we extend the definition of the adiabatic and non-adiabatic entropies introduced by M. Esposito and C. Van den Broeck in Phys. Rev. Lett. 104, 090601 (2010) for the stationary case. We also obtain interesting second-law like inequalities for transitions between non-stationary states.