Abstract
We follow recent developments of a finite size thermal field theoretic formalism, which is mainly relevant to the investigation of small size corrections to the thermodynamical properties of the quark-gluon plasma. In doing so, we rely on statistical mechanics and large deviation theory arguments, and investigate geometrically confined systems of infinite volume V with a finite spatial extent L. More specifically, we focus on systems in contact with a heat bath as well as on isolated ones. We find and present in detail the characteristic behaviors of a first and a second order phase transition, respectively. In the former case, we establish a connection between the phase transition and the mechanical support of the system. In the latter one, we identify a critical length Lc~(V/EL)1/3, where E is the total energy of the system which is fixed. We also briefly comment on the relevance of our findings, for respectively both the Casimir experiments and the future quark-gluon plasma phenomenology.
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