GENERIC formalism of a Vlasov-Fokker-Planck equation and connection to large-deviation principles

TL;DR

This paper explores the connection between a Vlasov-Fokker-Planck equation and microscopic particle systems within the GENERIC framework, providing a variational formulation and linking large deviations to non-reversible systems.

Contribution

It offers a variational formulation for GENERIC systems and explains the origins of its conditions, extending large-deviation principles to non-reversible particle systems.

Findings

Provides a variational formulation for GENERIC systems

Connects large-deviation principles to non-reversible particle systems

Explains the origin of degeneracy conditions in GENERIC

Abstract

In this paper we discuss the connections between a Vlasov-Fokker-Planck equation and an underlying microscopic particle system, and we interpret those connections in the context of the GENERIC framework (\"Ottinger 2005). This interpretation provides (a) a variational formulation for GENERIC systems, (b) insight into the origin of this variational formulation, and (c) an explanation of the origins of the conditions that GENERIC places on its constitutive elements, notably the so-called degeneracy or non-interaction conditions. This work shows how the general connection between large-deviation principles on one hand and gradient-flow structures on the other hand extends to non-reversible particle systems.