Negative Specific Heat in Astronomy, Physics and Chemistry

TL;DR

This paper reviews the concept of negative specific heat in gravitational and other systems, discussing its implications for thermodynamics, phase transitions, and applications beyond astrophysics.

Contribution

It clarifies the conditions for negative specific heat, corrects previous proofs, and links these phenomena to phase transitions and units in various physical systems.

Findings

Negative specific heat occurs in gravitating systems with certain density contrasts.

Microcanonical ensembles can exhibit negative heat capacity over specific energy ranges.

First order phase transitions may be caused by negative heat capacities of constituent units.

Abstract

Starting from Antonov's discovery that there is no maximum to the entropy of a gravitating system of point particles at fixed energy in a spherical box if the density contrast between centre and edge exceeds 709, we review progress in the understanding of gravitational thermodynamics. We pinpoint the error in the proof that all systems have positive specific heat and say when it can occur. We discuss the development of the thermal runaway in both the gravothermal catastrophe and its inverse. The energy range over which microcanonical ensembles have negative heat capacity is replaced by a first order phase transition in the corresponding canonical ensembles. We conjecture that all first order phase transitions may be viewed as caused by negative heat capacities of units within them. We find such units in the theory of ionisation, chemical dissociation and in the Van der Waals gas so these concepts are applicable outside the realm of stars, star clusters and black holes.