Dynamical Phase Transitions for Flows on Finite Graphs

We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate functional of the average flow is given by a variational formulation...

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Bibliographic Details
Published inJournal of statistical physics Vol. 181; no. 6; pp. 2353 - 2371
Main Authors Gabrielli, Davide, Renger, D. R. Michiel
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2020
Springer
Subjects
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
05C21
82C26
60F10
82C22
Particle systems
Large deviations
Phase transitions
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Summary:We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate functional of the average flow is given by a variational formulation involving paths of the density and flow. We give sufficient conditions under which the large deviations of a given time averaged flow is determined by paths that are constant in time. We then consider a class of models on a discrete ring for which it is possible to show that a better strategy is obtained producing a time-dependent path. This phenomenon, called a dynamical phase transition, is known to occur for some particle systems in the hydrodynamic scaling limit, which is thus extended to the setting of a finite graph.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-020-02667-0