Heterogeneity-induced large deviations in activity and (in some cases) entropy production

TL;DR

This paper analytically explores a simple model exhibiting a dynamic phase transition, revealing how heterogeneity influences activity and entropy production distributions, with implications for biological systems like bacterial responses.

Contribution

It introduces an analytical solution for a model with a dynamic phase transition influenced by heterogeneity, highlighting the role of symmetries in observing bistability.

Findings

Identification of two dynamical phases: localized and delocalized.

Analytical computation of joint rate functions for activity and entropy production.

Demonstration that certain distributions do not always reveal underlying phase transitions.

Abstract

We solve a simple model that supports a dynamic phase transition and show conditions for the existence of the transition. Using methods of large deviation theory we analytically compute the probability distribution for activity and entropy production rates of the trajectories on a large ring with a single heterogeneous link. The corresponding joint rate function demonstrates two dynamical phases - one localized and the other delocalized, but the marginal rate functions do not always exhibit the underlying transition. Symmetries in dynamic order parameters influence the observation of a transition, such that distributions for certain dynamic order parameters need not reveal an underlying dynamical bistability. Solution of our model system furthermore yields the form of the effective Markov transition matrices that generate dynamics in which the two dynamical phases are at coexistence. We discuss the implications of the transition for the response of bacterial cells to antibiotic treatment, arguing that even simple models of a cell cycle lacking an explicit bistability in configuration space will exhibit a bistability of dynamical phases.