Quantitative analysis of Clausius inequality

TL;DR

This paper analyzes the energy dissipation in driven diffusive systems during thermodynamic transformations, deriving optimal protocols that minimize energy loss and revealing that optimal paths involve inhomogeneous equilibrium states.

Contribution

It provides a quantitative expansion of the energy balance and characterizes minimal dissipation transformations, including the surprising result for ideal gases.

Findings

Optimal transformations are sequences of inhomogeneous equilibrium states.

Derived an expansion of energy balance for finite-time thermodynamic processes.

Identified the optimal correction to the quasi-static limit.

Abstract

In the context of driven diffusive systems, for thermodynamic transformations over a large but finite time window, we derive an expansion of the energy balance. In particular, we characterize the transformations which minimize the energy dissipation and describe the optimal correction to the quasi-static limit. Surprisingly, in the case of transformations between homogeneous equilibrium states of an ideal gas, the optimal transformation is a sequence of inhomogeneous equilibrium states.