Nonequilibrium Thermodynamics of the First and Second Kind: Averages and Fluctuations

TL;DR

This paper compares two approaches to nonequilibrium thermodynamics, focusing on their fluctuation relations and free energy differences, and highlights the Fokker-Planck equation's effectiveness in describing fluctuations.

Contribution

It provides a detailed comparison of the two-generator bracket formulation and macroscopic fluctuation theory, emphasizing the role of boundary conditions and the Fokker-Planck equation.

Findings

Fluctuation dissipation relations are crucial for comparing approaches.

Different boundary conditions lead to different nonequilibrium Helmholtz free energies.

Fokker-Planck equation effectively describes long-range fluctuations.

Abstract

We compare two approaches to nonequilibrium thermodynamics, the two-generator bracket formulation of time-evolution equations for averages and the macroscopic fluctuation theory, for an isothermal driven diffusive system under steady state conditions. The fluctuation dissipation relations of both approaches play an important role for a detailed comparison. The nonequilibrium Helmholtz free energies introduced in these two approaches differ as a result of boundary conditions. A Fokker-Planck equation derived by projection operator techniques properly reproduces long range fluctuations in nonequilibrium steady states and offers the most promising possibility to describe the physically relevant fluctuations around macroscopic averages for time-dependent nonequilibrium systems.