Fluctuation symmetry leads to GENERIC equations with non-quadratic dissipation

TL;DR

This paper reveals how fluctuation symmetry in Hamiltonians leads to GENERIC equations with non-quadratic dissipation, extending large-deviation theory to systems with inertia.

Contribution

It introduces a formalism linking fluctuation symmetry to GENERIC structures, broadening understanding of non-quadratic dissipation in complex systems.

Findings

GENERIC structure arises from Hamiltonian symmetry

Extension of large-deviation principles to inertial systems

Connection between stochastic fluctuations and deterministic dynamics

Abstract

We develop a formalism to discuss the properties of GENERIC systems in terms of corresponding Hamiltonians that appear in the characterization of large-deviation limits. We demonstrate how the GENERIC structure naturally arises from a certain symmetry in the Hamiltonian, which extends earlier work that has connected the large-deviation behaviour of reversible stochastic processes to the gradient-flow structure of their deterministic limit. Natural examples of application include particle systems with inertia.