Thermodynamics of histories for the one-dimensional contact process

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.

16 pages, 7 figures

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Cited by in corpus (11)

• Frenesy: time-symmetric dynamical activity in nonequilibria
• Current large deviations for driven periodic diffusions
• A minimal model of dynamical phase transition
• Finite-temperature critical point of a glass transition
• Diffusions conditioned on occupation measures
• Large deviations of ergodic counting processes: a statistical mechanics approach
• Finite size scaling of current fluctuations in the totally asymmetric exclusion process
• Space-time Phase Transitions in Driven Kinetically Constrained Lattice Models
• Thermodynamics of quantum jump trajectories in systems driven by classical fluctuations
• Space-time phase transitions in the East model with a softened kinetic constraint
• Breakdown of the Finite-Time and -Population Scalings of the Large Deviation Function in the Large-Size Limit of a Contact Process