Canonical Ensemble vs. Grand Canonical Ensemble in the Description of Multicomponent Bosonic Systems

Abstract

The thermodynamics of a system of interacting bosonic particles and antiparticles in the presence of the Bose–Einstein condensate is studied in the framework of a Skyrme-like mean-field model. It is assumed that the total charge density (isospin density) is conserved at all temperatures. Two cases are explicitly considered: the zero or nonzero isospin charge of the system. A comparative analysis is carried out using the Canonical Ensemble or the Grand Canonical Ensemble. It is shown that the Grand Canonical Ensemble is not suitable for describing the bosonic systems of particles and antiparticles in the presence of a condensate, but an adequate study can be carried out within the framework of the canonical ensemble, where the chemical potential is a thermodynamic quantity that depends on the canonical free variable.