Negativity of the Casimir Self-Entropy in Spherical Geometries

Yang Li; Kimball Milton; Prachi Parashar; Lujan Hong

doi:10.20944/preprints202101.0585.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 27 January 2021 / Approved: 28 January 2021 / Online: 28 January 2021 (13:15:37 CET)

It has been recognized for some time that even for perfect conductors, the interaction Casimir entropy, due to quantum/thermal fluctuations, can be negative. This result was not considered problematic because it was thought that the self-entropies of the bodies would cancel this negative interaction entropy, yielding a total entropy that was positive. In fact, this cancellation seems not to occur. The positive self entropy of a perfectly conducting sphere does indeed just cancel the negative interaction entropy of a system consisting of a perfectly conducting sphere and plate, but a model with weaker coupling in general possesses a regime where negative self-entropy appears. The physical meaning of this surprising result remains obscure. In this paper we re-examine these issues, using improved physical and mathematical techniques, partly based on the Abel-Plana formula, and present numerical results for arbitrary temperatures and couplings, which exhibit the same remarkable features.

Entropy; free energy; Casimir effect

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Negativity of the Casimir Self-Entropy in Spherical Geometries

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