On the origin of power-laws in equilibrium
  A particle in the attractive Coulomb field has an interesting property: its specific heat is constant and negative. We show, both analytically and numerically, that when a classical Hamiltonian system stays in weak contact with one such negative specific heat object, its statistics conforms to a fat-tailed power-law distribution with power index given by $C/k_B-1$, where $k_B$ is Boltzmann constant and $C$ is the heat capacity. 
Michele Campisi, Fei Zhan, and Peter H\"anggi
cond-mat.stat-mech