Modified fluctuation-dissipation and Einstein relation at non-equilibrium steady states

TL;DR

This paper derives unified modified fluctuation-dissipation relations for non-equilibrium steady states, showing their equivalence across different models and illustrating an additive correction to the Einstein relation with a molecular motor example.

Contribution

It provides a unified derivation of modified fluctuation-dissipation relations applicable to non-equilibrium steady states, connecting continuum and discrete models.

Findings

Unified derivation of MFDR for non-equilibrium steady states

Equivalence of velocity forms of MFDR from different dynamics

Additive correction to Einstein relation demonstrated with molecular motor model

Abstract

Starting from the pioneering work of G. S. Agarwal [Zeitschrift f\"ur Physik 252, 25 (1972)], we present a unified derivation of a number of modified fluctuation-dissipation relations (MFDR) that relate response to small perturbations around non-equilibrium steady states to steady-state correlations. Using this formalism we show the equivalence of velocity forms of MFDR derived using continuum Langevin and discrete master equation dynamics. The resulting additive correction to the Einstein relation is exemplified using a flashing ratchet model of molecular motors.