Threshold for everlasting initial memory in equilibration processes

TL;DR

This paper demonstrates that in certain non-equilibrium conditions, the large deviation function of time-integrated quantities retains initial memory indefinitely, challenging the conventional exponential decay assumption.

Contribution

It introduces a finite threshold in Brownian dynamics beyond which initial memory persists forever in the large deviation function.

Findings

Identifies a sharp threshold for everlasting initial memory in Brownian particles.

Shows initial memory can persist in large deviation functions even at infinite time.

Provides physical intuition and toy model analysis for the phenomenon.

Abstract

Conventional wisdom indicates that initial memory should decay away exponentially in time for general (noncritial) equilibration processes. In particular, time-integrated quantities such as heat are presumed to lose initial memory in a sufficiently long-time limit. However, we show that the large deviation function of time-integrated quantities may exhibit initial memory effect even in the infinite-time limit, if the system is initially prepared sufficiently far away from equilibrium. For a Brownian particle dynamics, as an example, we found a sharp finite threshold rigorously, beyond which the corresponding large deviation function contains everlasting initial memory. The physical origin for this phenomenon is explored with an intuitive argument and also from a toy model analysis.