Phase transitions in the unconstrained ensemble

TL;DR

This paper demonstrates that completely open systems can exhibit first-order phase transitions in the unconstrained ensemble, using a modified Thirring model with finite-sized particles, revealing ensemble inequivalence.

Contribution

It shows the existence of phase transitions in the unconstrained ensemble and compares these with other ensembles, highlighting ensemble inequivalence in open systems.

Findings

First-order phase transitions occur in the unconstrained ensemble.

Unconstrained and grand canonical ensembles are equivalent for the model.

Inequivalence is observed between unconstrained and isothermal-isobaric ensembles.

Abstract

The unconstrained ensemble describes completely open systems in which energy, volume and number of particles fluctuate. Here we show that not only equilibrium states can exist in this ensemble, but also that completely open systems can undergo first-order phase transitions. This is shown by studying a modified version of the Thirring model with attractive and repulsive interactions and with particles of finite size. The model exhibits first-order phase transitions in the unconstrained ensemble, at variance with the analogous model with point-like particles. While unconstrained and grand canonical ensembles are equivalent for this model, we found inequivalence between the unconstrained and isothermal-isobaric ensembles. By comparing the thermodynamic phase diagram in the unconstrained case with that obtained in the isothermal-isobaric ensemble, we show that phase transitions under completely open conditions for this model are different from those in which the number of particles is fixed, highlighting the inequivalence of ensembles.