  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.
