Thermodynamics of the Casimir Effect at low temperatures.

In 1948 Hendrik Casimir predicted the existence of an attractive force between two perfectly conducting and neutral parallel plates. This stunning finding is one of the most remarkable manifestations of the quantum vacuum fluctuations of the electromagnetic field. Since then the so-called Casimir effect has been extensively studied, and many theoretical and experimental advances have been achieved in this field.
In this work we present an alternative way to those presented by Brown & Maclay, to compute the electromagnetic stress-tensor in the region between the plates for finite temperatures as well as for the zero-temperature limit, and we connect its components with the thermodynamic quantities of the radiation field. Our major goal is to present a complete study of the thermodynamics of this system at low temperatures or small plate separation. We also briefly consider the high temperature or large plate separation limit, which reveals how the thermodynamics of the blackbody radiation may change under the presence of the zero-point energy.