Nonequilibrium stationary states and equilibrium models with long range interactions

Abstract

It was recently suggested by Blythe and Evans that a properly defined steady state normalisation factor can be seen as a partition function of a fictitious statistical ensemble in which the transition rates of the stochastic process play the role of fugacities. In analogy with the Lee-Yang description of phase transition of equilibrium systems, they studied the zeroes in the complex plane of the normalisation factor in order to find phase transitions in nonequilibrium steady states. We show that like for equilibrium systems, the ``densities'' associated to the rates are non-decreasing functions of the rates and therefore one can obtain the location and nature of phase transitions directly from the analytical properties of the ``densities''. We illustrate this phenomenon for the asymmetric exclusion process. We actually show that its normalisation factor coincides with an equilibrium partition function of a walk model in which the ``densities'' have a simple physical interpretation.

LaTeX, 23 pages, 3 EPS figures

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Cited by in corpus (17)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism
• Generic finite size scaling for discontinuous nonequilibrium phase transitions into absorbing states
• Dyck Paths, Motzkin Paths and Traffic Jams
• Continued Fractions and the Partially Asymmetric Exclusion Process
• Finite-size scaling for discontinuous nonequilibrium phase transitions
• Combinatorial mappings of exclusion processes
• An introduction to phase transitions in stochastic dynamical systems
• KPZ fluctuations in finite volume
• Refined Razumov-Stroganov conjectures for open boundaries
• Bose-Einstein condensation and a two-dimensional walk model
• Equivalence of a one-dimensional driven-diffusive system and an equilibrium two-dimensional walk model
• Simple Asymmetric Exclusion Model and Lattice Paths: Bijections and Involutions
• A heterogeneous zero-range process related to a two-dimensional walk model
• One-transit paths and steady-state of a non-equilibrium process in a discrete-time update
• Combinatorics of the three-parameter PASEP partition function
• Relaxation time in a non-conserving driven-diffusive system with parallel dynamics