Path integral approach to nonequilibrium potentials in multiplicative Langevin dynamics
1 Departamento de Física Teórica, Universidade do Estado do Rio de Janeiro Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil
2 Departamento de Matemática Aplicada, Universidade do Estado do Rio de Janeiro Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil
Received: 20 October 2015
Accepted: 14 January 2016
We present a path integral formalism to compute potentials for nonequilibrium steady states, reached by a multiplicative stochastic dynamics. We develop a weak-noise expansion, which allows the explicit evaluation of the potential in arbitrary dimensions and for any stochastic prescription. We apply this general formalism to study noise-induced phase transitions. We focus on a class of multiplicative stochastic lattice models and compute the steady-state phase diagram in terms of the noise intensity and the lattice coupling. We obtain, under appropriate conditions, an ordered phase induced by noise. By computing entropy production, we show that microscopic irreversibility is a necessary condition to develop noise-induced phase transitions. This property of the nonequilibrium stationary state has no relation with the initial stages of the dynamical evolution, in contrast with previous interpretations, based on the short-time evolution of the order parameter.
PACS: 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.20.-y – Classical statistical mechanics
© EPLA, 2016