  When addressing the thermodynamics of finite-sized systems, one must specify
whether one wants to fix conserved charges to a sharp value or whether one is
content to fix their thermodynamic average. In other words, contrary to the
thermodynamic limit, different statistical ensembles are not equivalent. When
treating the plasma phases of gauge field theories perturbatively in the
canonical ensemble, unexpected new difficulties arise in comparison with the
usual grand canonical treatment. The purpose of this paper is to expose these
difficulties and show how they can be remedied, thus recovering a well-defined
description of plasmas even in a finite-size, canonical ensemble setting. For
definiteness, a specific model is considered, namely QCD$_{1+1} $ with SU(2)
color; however, the treatment presented should be applicable also to
higher-dimensional systems with different types of Coulomb interaction.
