  Recent works have associated systems of particles, characterized by
short-range repulsive interactions and evolving under overdamped motion, to a
nonlinear Fokker-Planck equation within the class of nonextensive statistical
mechanics, with a nonlinear diffusion contribution whose exponent is given by
$\nu=2-q$. The particular case $\nu=2$ applies to interacting vortices in
type-II superconductors, whereas $\nu>2$ covers systems of particles
characterized by short-range power-law interactions, where correlations among
particles are taken into account. In the former case, several studies presented
a consistent thermodynamic framework based on the definition of an effective
temperature $\theta$ (presenting experimental values much higher than typical
room temperatures $T$, so that thermal noise could be neglected), conjugated to
a generalized entropy $s_{\nu}$ (with $\nu=2$). Herein, the whole thermodynamic
scheme is revisited and extended to systems of particles interacting
repulsively, through short-ranged potentials, described by an entropy
$s_{\nu}$, with $\nu>1$, covering the $\nu=2$ (vortices in type-II
superconductors) and $\nu>2$ (short-range power-law interactions) physical
examples. The main results achieved are: (a) The definition of an effective
temperature $\theta$ conjugated to the entropy $s_{\nu}$; (b) The construction
of a Carnot cycle, whose efficiency is shown to be
$\eta=1-(\theta_2/\theta_1)$, where $\theta_1$ and $\theta_2$ are the effective
temperatures associated with two isothermal transformations, with
$\theta_1>\theta_2$; (c) Thermodynamic potentials, Maxwell relations, and
response functions. The present thermodynamic framework, for a system of
interacting particles under the above-mentioned conditions, and associated to
an entropy $s_{\nu}$, with $\nu>1$, certainly enlarges the possibility of
experimental verifications.
