Negativity of the Casimir Self-Entropy in Spherical Geometries

Abstract

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.

Low-temperature expansion of the Casimir–Polder free energy for an atom interacting with a conductive plane

“…The temperature contribution for µ ≥ m is shown in Figure 4. We observe that for low temperatures the free energy has the form of parabola, ∼ G tm (aT ) 2 , in agreement with (30) with negative parameter G tm (see Figure 3). the greater value of the parameter of parabola G tm , in agreement with Figure 3.…”

“…[15,29] for plain and spherical configurations in the framework of plasma model and also was discussed recently in Ref. [30].…”

“…From the Figures 4,5 and relations (30) we observe the different signs of the entropy, S, for µ < m and µ > m. The entropy is the negative derivative of the free energy with respect of temperature. Therefore, S µ<m < 0 (see Figure 5) and S µ>m > 0 (see Figure 4).…”

Casimir Self-Entropy of Nanoparticles with Classical Polarizabilities: Electromagnetic Field Fluctuations

“…[26]. Most recently, we utilized a numerical method, based on the Abel-Plana formula, to elucidate general behaviors of PDS self-entropies [27], which confirms the results in Ref. [23] and clearly demonstrates the existence of negative self-entropy.…”

Negative Newton constant may destroy some conjectures

“…The negative entropy of horizon was discussed for a white hole obtained from the black hole with the same mass by quantum tunneling, 28,29 and in Einstein-Gauss-Bonnet gravity, 30,31 see also Ref. 32 and references therein. It is possible that if there is a meaningful notion of negative entropy, then the Jacobson approach may produce gravity with negative G. It would be interesting to consider the connection between the negative G and the negative S.…”