Transition from localized to delocalized trajectories in random walk subject to random drives

TL;DR

This paper investigates a random walk model under random drives, revealing a phase transition between localized and delocalized trajectories, with implications for understanding non-equilibrium behavior in physical and biological systems.

Contribution

The study introduces a numerical analysis of the phase transition in a random walk model under random drives, highlighting the distinct dynamical phases and their thermodynamic signatures.

Findings

Identification of localized and delocalized phases in the model

Distinct heat dissipation statistics for each phase

Insights into non-equilibrium phase behavior

Abstract

Random walk subject to random drive has been extensively employed as a model for physical and biological processes. While equilibrium statistical physics has yielded significant insights into the distributions of dynamical fixed points of such a system, its non-equilibrium properties remain largely unexplored. In contrast, most real-world applications concern the dynamical aspects of this model. In particular, dynamical quantities like heat dissipation and work absorption play a central role in predicting and controlling non-equilibrium phases of matter. Recent advances in non-equilibrium statistical physics enable a more refined study of the dynamical aspects of random walk under random drives. We perform a numerical study on this model and demonstrate that it exhibits two distinct phases: a localized phase where typical random walk trajectories are non-extensive and confined to the neighborhood of fixed points, and a delocalized phase where typical random walk trajectories are extensive and can transition between fixed points. We propose different summary statistics for the heat dissipation and show that these two phases are distinctly different. Our characterization of these distinctive phases deepens the understanding of and provides novel strategies for the non-equilibrium phase of this model.