Ensemble in-equivalence in supernova matter within a simple model

TL;DR

This paper introduces a simple exactly solvable model for supernova baryonic matter, revealing ensemble in-equivalence and phase transition phenomena relevant to supernova evolution.

Contribution

It presents a novel simple model capturing phase transition behavior and ensemble in-equivalence in supernova matter, highlighting effects of nuclear forces and electromagnetic interactions.

Findings

First order phase transition in grandcanonical ensemble

Ensemble in-equivalence with negative susceptibility

Discontinuities in conjugate observables

Abstract

A simple, exactly solvable statistical model is presented for the description of baryonic matter in the thermodynamic conditions associated to the evolution of core-collapsing supernova. It is shown that the model presents a first order phase transition in the grandcanonical ensemble which is not observed in the canonical ensemble. Similar to other model systems studied in condensed matter physics, this ensemble in-equivalence is accompanied by negative susceptibility and discontinuities in the intensive observables conjugated to the order parameter. This peculiar behavior originates from the fact that baryonic matter is subject to attractive short range strong forces as well as repulsive long range electromagnetic interactions, partially screened by a background of electrons. As such, it is expected in any theoretical treatment of nuclear matter in the stellar environment. Consequences for the phenomenology of supernova dynamics are drawn.