Thermodynamics of histories for the one-dimensional contact process

TL;DR

This paper investigates the dynamical phase transition in the one-dimensional contact process by analyzing the thermodynamics of histories weighted by activity, revealing a phase transition at a critical parameter s across all infection rates.

Contribution

It applies a density matrix renormalisation group approach to characterize the phase diagram and critical exponents of the activity-based thermodynamics in the contact process.

Findings

Identifies a phase transition at a critical s for all infection rates.

Shows scaling behavior of the activity generating function near the absorbing state.

Reveals similarities between activity thermodynamics and equilibrium critical phenomena.

Abstract

The dynamical activity K(t) of a stochastic process is the number of times it changes configuration up to time t. It was recently argued that (spin) glasses are at a first order dynamical transition where histories of low and high activity coexist. We study this transition in the one-dimensional contact process by weighting its histories by exp(sK(t)). We determine the phase diagram and the critical exponents of this model using a recently developed approach to the thermodynamics of histories that is based on the density matrix renormalisation group. We find that for every value of the infection rate, there is a phase transition at a critical value of s. Near the absorbing state phase transition of the contact process, the generating function of the activity shows a scaling behavior similar to that of the free energy in an equilibrium system near criticality.