Relaxation to nonequilibrium

TL;DR

This paper develops a theoretical framework for understanding the relaxation dynamics of driven macroscopic systems using a nonequilibrium extension of the Onsager-Machlup action, emphasizing the role of frenesy and thermodynamic forces.

Contribution

It introduces a nonequilibrium, nonlinear extension of the Onsager-Machlup formalism, highlighting the importance of frenesy and local detailed balance in macroscopic relaxation.

Findings

The structure of relaxation is characterized as a zero-cost flow.

The nonequilibrium entropy is shown to be monotone in time.

The approach extends GENERIC to nonequilibrium steady states.

Abstract

We describe the structure of relaxation for a steadily driven macroscopic body. The time-evolution is characterized as the zero-cost flow for a nonequilibrium and nonlinear extension of the Onsager-Machlup action governing the dynamical fluctuations. The approach hinges on two main elements: the principle of local detailed balance, which identifies the relevant thermodynamic forces, and the canonical decomposition of the frenesy into a Legendre pair. Notably, it is the time-symmetric component of the Lagrangian, the frenesy, that shapes the structure of the macroscopic evolution for given forcing. We add a simple argument for why the nonequilibrium entropy, which governs the static macroscopic fluctuations of the system, is monotone in time. The results can be interpreted as the steady nonequilibrium extension of GENERIC where relaxation to equilibrium is governed by a dissipative gradient flow superimposed on a Hamiltonian flow.