First-order phase transitions from poles in asymptotic representations of partition functions

TL;DR

This paper explores how poles in asymptotic series representations of partition functions relate to first-order phase transitions, providing a new method to identify nonconcave entropy regions beyond traditional free energy analysis.

Contribution

It demonstrates that poles in asymptotic expansions can reveal linear segments and nonconcavity in entropy, offering a novel approach to analyze phase transitions.

Findings

Poles correspond to linear branches of entropy.

Poles indicate nonconcave entropy regions.

Method distinguishes phase transition types.

Abstract

Although partition functions of finite-size systems are always analytic, and hence have no poles, they can be expressed in many cases as series containing terms with poles. Here we show that such poles can be related to linear branches of the entropy, expressed in the thermodynamic limit as a function of the energy per particle. We also show that these poles can be used to determine whether the entropy is nonconcave or has linear parts, which is something that cannot be done with the sole knowledge of the thermodynamic free energy derived from the partition function. We discuss applications for equilibrium systems having first-order phase transitions.