Conditions for negative specific heat in systems of attracting classical particles

TL;DR

This paper explores the conditions under which classical systems of attracting particles exhibit negative specific heat, focusing on the role of force potential parameters and system dimensions, with implications for understanding gravitational and long-range interactions.

Contribution

It identifies specific conditions, particularly the force potential exponent and spatial dimensions, that lead to negative specific heat in classical attracting particle systems, using analytical models and the Virial theorem.

Findings

Negative specific heat occurs at  for  in systems with  dimensions.

Negative specific heat is not solely due to long-range forces.

Negative specific heat appears when the force potential exponent  negative, without density singularities.

Abstract

We identify conditions for the presence of negative specific heat in non-relativistic self-gravitating systems and similar systems of attracting particles. The method used, is to analyse the Virial theorem and two soluble models of systems of attracting particles, and to map the sign of the specific heat for different combinations of the number of spatial dimensions of the system, $D$($\geq 2$), and the exponent, $\nu$($\neq 0$), in the force potential, $\phi=Cr^\nu$. Negative specific heat in such systems is found to be present exactly for $\nu=-1$, at least for $D \geq 3$. For many combinations of $D$ and $\nu$ representing long-range forces, the specific heat is positive or zero, for both models and the Virial theorem. Hence negative specific heat is not caused by long-range forces as such. We also find that negative specific heat appears when $\nu$ is negative, and there is no singular point in a certain density distribution. A possible mechanism behind this is suggested.