Linear approximations of large deviations: Cubic diffusion test

TL;DR

This paper introduces a linearization method to approximate large deviation rate functions for diffusion processes, effectively capturing fluctuations in nonequilibrium systems, especially for large deviations.

Contribution

The paper presents a novel linear approximation technique for large deviation rate functions in diffusion processes, tested on a nonlinear cubic drift model.

Findings

Linear approximation aligns well with exact rate functions.

Accuracy improves with better localization of the linearized process.

Method is effective for large fluctuation regimes.

Abstract

We propose a method for approximating the large deviation rate function of time-integrated observables of diffusion processes, used in statistical physics to characterize the fluctuations of nonequilibrium systems. The method is based on linearizing the effective process associated with the large deviations of the process and observable considered, and is tested for a simple one-dimensional nonlinear diffusion model involving a cubic drift. The results show that the linear approximation compares well with the exact rate function, especially in the large fluctuation regime, and that its accuracy is related to the way the linearized process localizes in space. Possible extensions and applications to more complex diffusion models are proposed for future work.