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The driving force of the dynamical system can be decomposed into the gradientof a potential landscape and curl flux (current). The fluctuation-dissipationtheorem (FDT) is often applied to near equilibrium systems with detailedbalance. The response due to a small perturbation can be expressed by aspontaneous fluctuation. For non-equilibrium systems, we derived a generalizedFDT that the response function is composed of two parts: (1) a spontaneouscorrelation representing the relaxation which is present in the nearequilibrium systems with detailed balance; (2) a correlation related to thepersistence of the curl flux in steady state, which is also in part linked to ainternal curvature of a gauge field. The generalized FDT is also related to thefluctuation theorem. In the equal time limit, the generalized FDT naturallyleads to non-equilibrium thermodynamics where the entropy production rate canbe decomposed into spontaneous relaxation driven by gradient force and housekeeping contribution driven by the non-zero flux that sustains thenon-equilibrium environment and breaks the detailed balance.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

Potential and Flux Decomposition for Dynamical Systems and  Non-Equilibrium Thermodynamics: Curvature, Gauge Field and Generalized  Fluctuation-Dissipation Theorem