Minimal Model of Stochastic Athermal Systems: Origin of Non-Gaussian Noise

TL;DR

This paper develops a minimal Langevin-like model with non-Gaussian noise to describe athermal systems, providing explicit conditions for non-Gaussian dominance and an inverse method to infer bath properties from tracer statistics.

Contribution

It introduces a new asymptotic expansion from master equations, deriving a minimal non-Gaussian Langevin model for athermal systems and an inverse formula for bath inference.

Findings

Derived explicit condition for non-Gaussian noise dominance

Applied model to granular motor and obtained velocity distribution

Demonstrated non-Gaussian Langevin equation as minimal athermal model

Abstract

For a wide class of stochastic athermal systems, we derive Langevin-like equations driven by non-Gaussian noise, starting from master equations and developing a new asymptotic expansion. We found an explicit condition whereby the non-Gaussian properties of the athermal noise become dominant for tracer particles associated with both thermal and athermal environments. Furthermore, we derive an inverse formula to infer microscopic properties of the athermal bath from the statistics of the tracer particle. We apply our formulation to a granular motor under viscous friction, and analytically obtain the angular velocity distribution function. Our theory demonstrates that the non-Gaussian Langevin equation is the minimal model of athermal systems.