We will develop a general formalism to compute finite temperature corrections to the quantum vacuum energy as well as the entropy for periodic classical background potentials represented by infinite chains of potentials with compact support. The present paper is a continuation of the above line of research concerning entropy in simple systems, now on periodic background fields. However, that is beyond the scope of the present paper. Now, one could speculate that negative entropy, like negative specific heat, could signal some instability of the system as discussed, for example, in. In all these cases the single standing objects were considered and the complete entropy, except the black body part (contributions from the empty space), was computed. For three dimensional ones, a plasma plane or a plasma sphere, in and and for some simple one dimensional examples in. In the last 3 years, the entropy of Casimir effect related configurations was calculated for quite a large number of model systems. This problem remains still unresolved and it is related to the choice of plasma or Drude model in Casimir force calculations, see for the actual status. However, not much attention was paid to since there only the separation dependent part of the entropy was considered and the focus was on another, possibly related, effect namely a violation of the Nernst’s heat theorem while using the Drude model for the dielectric slab. In fact, thermodynamic puzzles were observed earlier, see, e.g. Nearly 15 years ago in Casimir effect investigations the occurrence of negative entropy was noticed in.

In particular general boundary conditions were used to mimic idealised models of two plane parallel plates with arbitrary physical properties and topology changes (see Refs. In the last decade the use of boundary conditions allowed by the principles of quantum field theory has been used to study the properties and sign of the quantum vacuum energy.

Most of the results obtained have focused on the study of the dependence of the zero-temperature quantum vacuum energy and its sign with the geometry (see Refs.

Since the seminal work by Casimir and the experimental confirmation by Sparnay the theory of quantum fields interaction with classical backgrounds mimicking macroscopical objects has been a very active field of research (see Refs.

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