Observable Dependent Quasi-Equilibrium in Slow Dynamics

TL;DR

This paper investigates the non-equilibrium fluctuation-dissipation ratio in slow dynamics systems, showing that quasi-equilibrium behavior is not universal and depends on the observable and system state.

Contribution

It provides detailed analysis of the fluctuation-dissipation ratio in a Glauber-Ising spin chain, revealing violations of quasi-equilibrium behavior in certain observables.

Findings

X(t,tw) differs from 1 in the short-time regime

X(tw,tw) approaches 3/4 as tw increases

Violations of quasi-equilibrium behavior occur for defect observables

Abstract

We present examples demonstrating that quasi-equilibrium fluctuation-dissipation behavior at short time differences is not a generic feature of systems with slow non-equilibrium dynamics. We analyze in detail the non-equilibrium fluctuation-dissipation ratio X(t,tw) associated with a defect-pair observable in the Glauber-Ising spin chain. It turns out that $X \neq 1$ throughout the short-time regime and in particular X(tw,tw) = 3/4 for $tw \to \infty$. The analysis is extended to observables detecting defects at a finite distance from each other, where similar violations of quasi-equilibrium behaviour are found. We discuss our results in the context of metastable states, which suggests that a violation of short-time quasi-equilibrium behavior could occur in general glassy systems for appropriately chosen observables.