Affine relationships between steady currents

Abstract

Perturbing transition rates in a steady nonequilibrium system, e.g. modelled by a Markov jump process, causes a change in the local currents. Their susceptibility is usually expressed via Green-Kubo relations or their nonequilibrium extensions. However, we may also wish to directly express the mutual relation between currents. Such a nonperturbative interrelation was discovered by P.E. Harunari et al. in [1] by applying algebraic graph theory showing the mutual linearity of currents over different edges in a graph. We give a novel and shorter derivation of that current relationship where we express the current-current susceptibility as a difference in mean first-passage times. It allows an extension to multiple currents, which remains affine but the relation is not additive.

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• On the Poisson equation for nonreversible Markov jump processes

Cited by in corpus (6)

• Mutual Multilinearity of Nonequilibrium Network Currents
• Nonequilibrium fluctuation-response relations for state-current correlations
• Nonequilibrium fluctuation-response relations for state observables
• Macroscopic fluctuation-response theory and its use for gene regulatory networks
• Mutual Linearity is a Generic Property of Steady-State Markov Networks
• Thermodynamic Geometric Constraint on the Spectrum of Markov Rate Matrices