Nonequilibrium dynamics of a pure dry friction model subjected to coloured noise

TL;DR

This paper explores how coloured noise influences the nonequilibrium dynamics of a dry friction model, revealing stick-slip phenomena and probability currents through analytical and spectral analysis.

Contribution

It introduces a detailed analysis of a dry friction system under coloured noise, highlighting the role of noise correlation time in nonequilibrium behavior and stick-slip transitions.

Findings

Finite noise correlation time induces nontrivial probability currents.

Stick-slip phenomena are linked to a critical noise correlation time.

Analytic methods elucidate the transition mechanisms in the system.

Abstract

We investigate the impact of noise on a two-dimensional simple paradigmatic piecewise-smooth dynamical system. For that purpose we consider the motion of a particle subjected to dry friction and coloured noise. The finite correlation time of the noise provides an additional dimension in phase space, a nontrivial probability current, and thus establishes a proper nonequilibrium regime. Furthermore, the finite noise correlation time allows for the study of stick-slip phenomena which show up as a singular component in the stationary probability density. Analytic insight can be provided by application of the unified coloured noise approximation, developed by Jung and H\"anggi (Phys. Rev. A 35, 4464 (R) (1987)). The analysis of probability currents and a closer look at power spectral densities underpin the observed stick-slip transitions which are related with a critical value of the noise correlation time.