Path Integral approach to nonequilibrium potentials in multiplicative Langevin dynamics

TL;DR

This paper introduces a path integral formalism for calculating potentials in nonequilibrium steady states of multiplicative Langevin systems, enabling analysis of noise-induced phase transitions and the role of irreversibility.

Contribution

It develops a general weak-noise expansion method for arbitrary dimensions and stochastic prescriptions, applied to noise-induced phase transitions in lattice models.

Findings

Ordered phase induced by noise under certain conditions

Microscopic irreversibility is necessary for noise-induced transitions

The formalism allows explicit potential evaluation in complex systems

Abstract

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.