Non-monotonic temperature dependence of chaos-assisted diffusion in driven periodic systems

TL;DR

This paper reveals a non-monotonic relationship between temperature and diffusion in driven periodic systems, showing diffusion can decrease with increasing temperature due to deterministic chaos mechanisms.

Contribution

It uncovers a novel non-equilibrium phenomenon where diffusion decreases with temperature, linked to unstable periodic orbits within chaotic attractors, supported by numerical and simplified models.

Findings

Diffusion decreases with increasing temperature in certain driven systems.

Chaotic dynamics and unstable periodic orbits influence diffusion behavior.

The mechanism may be applicable to various natural and artificial systems.

Abstract

The spreading of a cloud of independent Brownian particles typically proceeds more effectively at higher temperatures, as it derives from the commonly known Sutherland-Einstein relation for systems in thermal equilibrium. Here, we report on a non-equilibrium situation in which the diffusion of a periodically driven Brownian particle moving in a periodic potential decreases with increasing temperature within a finite temperature window. We identify as the cause for this non-intuitive behaviour a dominant deterministic mechanism consisting of a few unstable periodic orbits embedded into a chaotic attractor together with thermal noise-induced dynamical changes upon varying temperature. The presented analysis is based on extensive numerical simulations of the corresponding Langevin equation describing the studied setup as well as on a simplified stochastic model formulated in terms of a three-state Markovian process. Because chaos exists in many natural as well as in artificial systems representing abundant areas of contemporary knowledge, the described mechanism may potentially be discovered in plentiful different contexts.