Minimum Dissipation Principle in Nonlinear Transport

TL;DR

This paper generalizes Onsager's minimum dissipation principle to nonlinear, non-equilibrium stationary states with local constraints, incorporating force decomposition and nonlinear transport coefficients.

Contribution

It extends the principle to nonlinear transport with force decomposition, allowing for force-dependent coefficients and microscopic irreversibility.

Findings

Application to 2D nonlinear diffusion with reservoirs at different temperatures

Inclusion of nonlinear flux-force relationships

Difference from Bertini et al. by assuming irreversibility

Abstract

We extend Onsager's minimum dissipation principle to stationary states that are only subject to local equilibrium constraints, even when the transport coefficients depend on the thermodynamic forces. Crucial to this generalization is a decomposition of the thermodynamic forces into those that are held fixed by the boundary conditions, and the subspace which is orthogonal with respect to the metric defined by the transport coefficients. We are then able to apply Onsager and Machlup's proof to the second set of forces. As an example we consider two-dimensional nonlinear diffusion coupled to two reservoirs at different temperatures. Our extension differs from that of Bertini et al. in that we assume microscopic irreversibility and we allow a nonlinear dependence of the fluxes on the forces.