Linear response theory in stochastic many-body systems revisited

TL;DR

This paper offers pedagogical proofs of fundamental linear response relations in stochastic many-body systems, clarifying their origins and interconnections, thus enhancing understanding of nonequilibrium statistical mechanics.

Contribution

It provides clear, pedagogical proofs of the Green-Kubo, Einstein, and fluctuation-response relations, elucidating their derivations and interrelations in stochastic many-body systems.

Findings

Green-Kubo relation derived from local detailed balance

Fluctuation-response relation extends equilibrium relations dynamically

Einstein relation explained via thermodynamics

Abstract

The Green-Kubo relation, the Einstein relation, and the fluctuation-response relation are representative universal relations among measurable quantities that are valid in the linear response regime. We provide pedagogical proofs of these universal relations for stochastic many-body systems. Through these simple proofs, we characterize the three relations as follows. The Green-Kubo relation is a direct result of the local detailed balance condition, the fluctuation-response relation represents the dynamic extension of both the Green-Kubo relation and the fluctuation relation in equilibrium statistical mechanics, and the Einstein relation can be understood by considering thermodynamics. We also clarify the interrelationships among the universal relations.