Overdamped dynamics of particles with repulsive power-law interactions
We investigate the dynamics of overdamped D-dimensional systems of particles repulsively interacting through short-ranged power-law potentials, V(r)∼r−λ(λ/D>1). We show that such systems obey a non-linear diffusion equation, and that their stationary state extremizes a q-generalized nonadditive entropy.
Here we focus on the dynamical evolution of these systems. Our first-principle D=1,2 many-body numerical simulations (based on Newton’s law) confirm the predictions obtained from the time-dependent solution of the non-linear diffusion equation, and show that the one-particle space-distribution P(x,t) appears to follow a compact-support q-Gaussian form, with q=1−λ/D.
We also calculate the velocity distributions P(vx,t) and, interestingly enough, they follow the same q-Gaussian form (apparently precisely for D=1, and nearly so for D=2). The satisfactory match between the continuum description and the molecular dynamics simulations in a more general, time-dependent, framework neatly confirms the idea that the present dissipative systems indeed represent suitable applications of the q-generalized thermostatistical theory.
A. A. Moreira, C. M. Vieira, H. A. Carmona, J. S. Andrade Jr., C. Tsallis, Overdamped dynamics of particles with repulsive power-law interactions, Phys. Rev. E 98 (2018) 032138