Fluctuation-dissipation relations far from equilibrium

TL;DR

This paper extends the fluctuation-dissipation theorem to systems far from equilibrium by mapping dissipative stochastic systems to Hamiltonian systems, providing new theoretical insights and potential applications in biological networks.

Contribution

It derives a generalized fluctuation-dissipation relation for nonequilibrium dissipative systems using a novel mapping to Hamiltonian systems.

Findings

Derived the F-D theorem for nonequilibrium dissipative systems.

Validated the theorem with several example systems.

Suggested applications in biological network analysis.

Abstract

The fluctuation-dissipation (F-D) theorem is a fundamental result for systems near thermodynamic equilibrium, and justifies studies between microscopic and macroscopic properties. It states that the nonequilibrium relaxation dynamics is related to the spontaneous fluctuation at equilibrium. Most processes in Nature are out of equilibrium, for which we have limited theory. Common wisdom believes the F-D theorem is violated in general for systems far from equilibrium. Recently we show that dynamics of a dissipative system described by stochastic differential equations can be mapped to that of a thermostated Hamiltonian system, with a nonequilibrium steady state of the former corresponding to the equilibrium state of the latter. Her we derived the corresponding F-D theorem, and tested with several examples. We suggest further studies exploiting the analogy between a general dissipative system appearing in various science branches and a Hamiltonian system. Especially we discussed the implications of this work on biological network studies.