Modified fluctuation-dissipation theorem near non-equilibrium states and applications to the Glauber-Ising chain

TL;DR

This paper derives a generalized modified fluctuation-dissipation theorem applicable to non-stationary non-equilibrium states, supported by theoretical derivations and illustrated through examples including a Brownian particle and the 1D Glauber-Ising model.

Contribution

It extends the MFDT to arbitrary non-stationary states using linear response and fluctuation theorems, with trajectory-level interpretation and practical examples.

Findings

Derived a general MFDT for non-stationary states

Connected MFDT to trajectory entropy concepts

Validated framework with solvable models

Abstract

In this paper, we present a general derivation of a modified fluctuation-dissipation theorem (MFDT) valid near an arbitrary non-stationary state for a system obeying markovian dynamics. We show that the method to derive modified fluctuation-dissipation theorems near non-equilibrium stationary states used by J. Prost et al., PRL 103, 090601 (2009), is generalizable to non-stationary states. This result follows from both standard linear response theory and from a transient fluctuation theorem, analogous to the Hatano-Sasa relation. We show that this modified fluctuation-dissipation theorem can be interpreted at the trajectory level using the notion of stochastic trajectory entropy, in a way which is similar to what has been done recently in the case of MFDT near non-equilibrium steady states (NESS). We illustrate this framework with two solvable examples: the first example corresponds to a brownian particle in an harmonic trap submitted to a quench of temperature and to a time-dependent stiffness. The second example is a classic model of coarsening systems, namely the 1D Ising model with Glauber dynamics.