Thermodynamic nonextensivity in a closed string gas

TL;DR

This paper investigates the thermodynamic properties of a closed string gas, revealing how nonextensivity leads to negative specific heat in microcanonical ensembles and discussing implications for canonical descriptions.

Contribution

It provides a detailed computation linking nonextensivity to negative specific heat in closed string gases, clarifying differences between microcanonical and canonical ensembles.

Findings

Negative specific heat occurs in microcanonical ensemble without winding modes.

Nonextensivity explains the negative specific heat in string gases.

Canonical ensemble cannot exhibit negative specific heat.

Abstract

Well known results in string thermodynamics show that there is always a negative specific heat phase in the microcanonical description of a gas of closed free strings whenever there are no winding modes present. We will carefully compute the number of strings in the gas to show how this negative specific heat is related to the fact that the system does not have thermodynamic extensivity. We will also discuss the consequences for a system of having a microcanonical negative specific heat versus the exact result that such a thing cannot happen in any canonical (fixed temperature) description.