Large deviations and gradient flows

TL;DR

This paper explores the connection between macroscopic gradient flows and microscopic large deviation principles, suggesting a broader framework for deriving entropies and free energies in non-equilibrium systems.

Contribution

It generalizes the link between gradient flows and large deviations beyond equilibrium, offering new insights into non-equilibrium thermodynamics.

Findings

Connected macroscopic gradient flows with large deviation principles.

Indicated potential to derive entropies and free energies from large deviations.

Extended known equilibrium relationships to non-equilibrium situations.

Abstract

In recent work [1] we uncovered intriguing connections between Otto's characterisation of diffusion as entropic gradient flow [16] on one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other. In this paper, we sketch this connection, show how it generalises to a wider class of systems, and comment on consequences and implications. Specifically, we connect macroscopic gradient flows with large deviation principles, and point out the potential of a bigger picture emerging: we indicate that in some non- equilibrium situations, entropies and thermodynamic free energies can be derived via large deviation principles. The approach advocated here is different from the established hydrodynamic limit passage but extends a link that is well known in the equilibrium situation.