title: Long-range interacting systems in the unconstrained ensemble.
abstract: Completely open systems can exchange heat, work, and matter with the environment. While energy, volume, and number of particles fluctuate under completely open conditions, the equilibrium states of the system, if they exist, can be specified using the temperature, pressure, and chemical potential as control parameters. The unconstrained ensemble is the statistical ensemble describing completely open systems and the replica energy is the appropriate free energy for these control parameters from which the thermodynamics must be derived. It turns out that macroscopic systems with short-range interactions cannot attain equilibrium configurations in the unconstrained ensemble, since temperature, pressure, and chemical potential cannot be taken as a set of independent variables in this case. In contrast, we show that systems with long-range interactions can reach states of thermodynamic equilibrium in the unconstrained ensemble. To illustrate this fact, we consider a modification of the Thirring model and compare the unconstrained ensemble with the canonical and grand-canonical ones: The more the ensemble is constrained by fixing the volume or number of particles, the larger the space of parameters defining the equilibrium configurations.
authors.affiliation: Laboratoire Charles Fabry, UMR 8501, Institut d'Optique, CNRS, Université Paris-Saclay, 2 Avenue Augustin Fresnel, 91127 Palaiseau Cedex, France.
authors.forename: Ivan
authors.initials: I
authors.lastname: Latella
authors.affiliation: Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain.
authors.forename: Agustín
authors.initials: A
authors.lastname: Pérez-Madrid
authors.affiliation: Complex Systems and Theoretical Physics Unit, Health and Technology Department, Istituto Superiore di Sanità, and INFN Roma 1, Viale Regina Elena 299, 00161 Roma, Italy.
authors.forename: Alessandro
authors.initials: A
authors.lastname: Campa
authors.affiliation: Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, and INFN, Sezione di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy.|INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy.
authors.forename: Lapo
authors.initials: L
authors.lastname: Casetti
authors.affiliation: SISSA, via Bonomea 265, ISC-CNR and INFN, 34136 Trieste, Italy.
authors.forename: Stefano
authors.initials: S
authors.lastname: Ruffo