General continuum approach for dissipative systems of repulsive particles

TL;DR

This paper introduces a general coarse-graining method to derive continuum equations for dissipative systems of repulsive particles, incorporating correlations and revealing links to Tsallis thermostatistics, with applications to vortices and plasma.

Contribution

A novel coarse-graining approach that accounts for correlations and connects to Tsallis statistics for short-range repulsive particle systems.

Findings

Derivation of a non-linear diffusion equation for overdamped dynamics.

Identification of a link between particle energy and Tsallis thermostatistics.

Validation through comparison with molecular dynamics simulations.

Abstract

We propose a general coarse-graining method to derive a continuity equation that describes any dissipative system of repulsive particles interacting through short-ranged potentials. In our approach, the effect of particle-particle correlations is incorporated to the overall balance of energy, and a non-linear diffusion equation is obtained to represent the overdamped dynamics. In particular, when the repulsive interaction potential is a short-ranged power-law, our approach reveals a distinctive correspondence between particle-particle energy and the generalized thermostatistics of Tsallis for any non-positive value of the entropic index q. Our methodology can also be applied to microscopic models of superconducting vortices and complex plasma, where particle-particle correlations are pronounced at low concentrations. The resulting continuum descriptions provide elucidating and useful insights on the microdynamical behavior of these physical systems. The consistency of our approach is demonstrated by comparison with molecular dynamics simulations.