Rare switching events in non-stationary systems

TL;DR

This paper explores how to extend the concept of transition rates between metastable states to non-stationary and memory-dependent physical systems, providing microscopic expressions for measuring these rates.

Contribution

It introduces a framework for defining and measuring time-dependent and history-dependent transition rates in non-stationary systems.

Findings

Identifies regimes where time-dependent rates are meaningful

Provides microscopic formulas for measuring rates

Extends metastable state transition theory to non-stationary systems

Abstract

Physical systems with many degrees of freedom can often be understood in terms of transitions between a small number of metastable states. For time-homogeneous systems with short-term memory these transitions are fully characterized by a set of rate constants. We consider the question how to extend such a coarse-grained description to non-stationary systems and to systems with finite memory. We identify the physical regimes in which time-dependent rates are meaningful, and state microscopic expressions that can be used to measure both externally time-dependent and history-dependent rates in microscopic simulations.