Bistable stochastic processes in the q-exponential family

TL;DR

This paper explores bistable stochastic systems with stationary distributions in the q-exponential family, comparing Langevin and superstatistical models, highlighting differences under quadratic multiplicative noise and transient behaviors.

Contribution

It introduces the analysis of quadratic multiplicative noise in Langevin models and compares stationary and transient properties with superstatistical models.

Findings

Stationary distribution under quadratic noise matches maximum Tsallis entropy predictions.

Stationary distributions of Langevin and superstatistical models are identical.

Transient behaviors differ significantly, as shown by mean first passage times.

Abstract

Stochastic bistable systems whose stationary distributions belong to the q-exponential family are investigated using two approaches: (i) the Langevin model subjected to additive and quadratic multiplicative noise, and (ii) the superstatistical model. Previously, the bistable Langevin model has been analyzed under linear multiplicative noise, whereas this paper reports on quadratic multiplicative noise, which is more physically meaningful. The stationary distribution of the Langevin model under quadratic multiplicative noise, which agrees with that derived by the maximum Tsallis entropy method, is found to be qualitatively different from its counterpart under linear multiplicative noise. We also show that the stationary distribution of the superstatistical model is the same as that of the Langevin model, whereas their transient properties, described in terms of mean first passage times (MFPTs), are qualitatively different.