An expression of excess work during transition between nonequilibrium steady states

TL;DR

This paper derives a macroscopic expression for excess work during quasistatic transitions between nonequilibrium steady states, linking thermodynamics, response functions, and microscopic physics.

Contribution

It introduces a new line integral expression for excess work in NESS transitions using linear response theory and connects macroscopic and microscopic descriptions.

Findings

Derived a line integral expression for excess work in NESS transitions.

Established a relationship between the vector potential and response functions.

Connected macroscopic thermodynamics to microscopic physics through response functions.

Abstract

Excess work is a non-diverging part of the work during transition between nonequilibrium steady states (NESSs). It is a central quantity in the steady state thermodynamics (SST), which is a candidate for nonequilibrium thermodynamics theory. We derive an expression of excess work during quasistatic transitions between NESSs by using the macroscopic linear response relation of NESS. This expression is a line integral of a vector potential in the space of control parameters. We show a relationship between the vector potential and the response function of NESS, and thus obtain a relationship between the SST and a macroscopic quantity. We also connect the macroscopic formulation to microscopic physics through a microscopic expression of the nonequilibrium response function, which gives a result consistent with the previous studies.