A numerical approach to large deviations in continuous-time

TL;DR

This paper introduces a direct continuous-time algorithm for evaluating large deviation functions in history-dependent observables, especially useful for systems with multiple time scales, and demonstrates its effectiveness in detecting dynamical phase transitions.

Contribution

The authors develop a continuous-time algorithm for large deviation functions that avoids time discretization, extending previous methods and improving efficiency with a thermodynamic-integration scheme.

Findings

Effective in systems with multiple time scales

Able to detect non-analyticities indicating phase transitions

Enhanced computational efficiency

Abstract

We present an algorithm to evaluate the large deviation functions associated to history-dependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm, valuable for systems with multiple time scales, thus extending the work of Giardin\`a, Kurchan and Peliti (PRL 96, 120603 (2006)). The procedure is supplemented with a thermodynamic-integration scheme, which improves its efficiency. We also show how the method can be used to probe large deviation functions in systems with a dynamical phase transition -- revealed in our context through the appearance of a non-analyticity in the large deviation functions.