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We propose a general coarse-graining method to derive a continuity equationthat describes any dissipative system of repulsive particles interactingthrough short-ranged potentials. In our approach, the effect ofparticle-particle correlations is incorporated to the overall balance ofenergy, and a non-linear diffusion equation is obtained to represent theoverdamped dynamics. In particular, when the repulsive interaction potential isa short-ranged power-law, our approach reveals a distinctive correspondencebetween particle-particle energy and the generalized thermostatistics ofTsallis for any non-positive value of the entropic index q. Our methodology canalso be applied to microscopic models of superconducting vortices and complexplasma, where particle-particle correlations are pronounced at lowconcentrations. The resulting continuum descriptions provide elucidating anduseful insights on the microdynamical behavior of these physical systems. Theconsistency of our approach is demonstrated by comparison with moleculardynamics simulations.

General continuum approach for dissipative systems of repulsive particles