On the origin of power-laws in equilibrium

TL;DR

This paper demonstrates that classical Hamiltonian systems in weak contact with negative specific heat objects exhibit fat-tailed power-law distributions, linking the power index to the heat capacity.

Contribution

It analytically and numerically establishes a direct connection between negative specific heat and power-law statistical distributions in equilibrium.

Findings

Classical systems in contact with negative specific heat objects follow power-law distributions.

The power-law index is given by $C/k_B - 1$, where $C$ is the heat capacity.

Negative specific heat leads to fat-tailed equilibrium statistics.

Abstract

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.