  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.
