Negative entropies in Casimir and Casimir‐Polder interactions

Milton, Kimball A.; Li, Yang; Kalauni, Pushpa; Parashar, Prachi; Guérout, R.; Ingold, Gert‐Ludwig; Lambrecht, Astrid; Reynaud, Serge

doi:10.1002/prop.201600047

Cited by 23 publications

(18 citation statements)

References 25 publications

(32 reference statements)

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“…But, indeed, it turned out that the sphere-plane problem was resolved by considering the self-entropy of the plate and the sphere separately. The former vanishes in the perfectly conducting limit, but the latter is just such as to cancel the most negative contribution of the interaction entropy [13,14]. The sphere-sphere entropy is then seen to be clearly positive as well.…”

Section: Introductionmentioning

confidence: 91%

Negativity of the Casimir Self-Entropy in Spherical Geometries

Li¹,

Milton²,

Parashar³

et al. 2021

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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.

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Section: Introductionmentioning

confidence: 91%

Negativity of the Casimir Self-Entropy in Spherical Geometries

Li¹,

Milton²,

Parashar³

et al. 2021

Preprint

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“…This is reached, however, by disregarding the real physical phenomena -the dissipation of conduction electrons for metals and the dc conductivity for dielectrics. That is why the above problems have been called in the literature the Casimir puzzle and the Casimir conundrum [43][44][45][46][47]. Taking into account that for metals and dielectrics the above inconsistencies originate from different sources (see below), it was suggested [43,47] to call them a puzzle and a conundrum, respectively.…”

Section: Introductionmentioning

confidence: 99%

Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution

Mostepanenko

2021

Universe

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This paper provides a review of the complicated problems in Lifshitz theory describing the Casimir force between real material plates composed of metals and dielectrics, including different approaches to their resolution. For both metallic plates with perfect crystal lattices and any dielectric plates, we show that the Casimir entropy calculated in the framework of Lifshitz theory violates the Nernst heat theorem when the well-approved dielectric functions are used in computations. The respective theoretical Casimir forces are excluded by the measurement data of numerous precision experiments. In the literature, this situation has been called the Casimir puzzle and the Casimir conundrum for the cases of metallic and dielectric plates, respectively. This review presents a summary of both the main theoretical and experimental findings on this subject. Next, a discussion is provided of the main approaches proposed in the literature to bring the Lifshitz theory into agreement with the measurement data and with the laws of thermodynamics. Special attention is paid to the recently suggested spatially nonlocal Drude-like response functions, which consider the relaxation properties of conduction electrons, as does the standard Drude model, but lead to the theoretical results being in agreement with both thermodynamics and the measurement data through the alternative response to quantum fluctuations of the mass shell. Further advances and trends in this field of research are discussed.

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“…This was borne out to some extent in the case of perfect conducting spheres. There it turned out that although the self-entropy of a conducting plate vanishes, the self-entropy of a conducting sphere is positive and is such that it precisely cancels the most negative interaction entropy between a sphere and a plate [14,15]. More specifically, the two electromagnetic mode contributions to the entropy, the TE and TM terms, had opposite signs: As expected [16], the TE was always negative, and the TM positive, the latter dominating the former.In this paper, we carry the sphere self-entropy problem much further.…”

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confidence: 99%

Casimir self-entropy of a spherical electromagnetic δ -function shell

et al. 2017

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In this paper we continue our program of computing Casimir self-entropies of idealized electrical bodies. Here we consider an electromagnetic δ-function sphere ("semitransparent sphere") whose electric susceptibility has a transverse polarization with arbitrary strength. Dispersion is incorporated by a plasma-like model. In the strong coupling limit, a perfectly conducting spherical shell is realized. We compute the entropy for both low and high temperatures. The TE self-entropy is negative as expected, but the TM self-entropy requires ultraviolet and infrared subtractions, and, surprisingly, is only positive for sufficiently strong coupling. Results are robust under different regularization schemes. I. INTRODUCTIONThe usual expectation, based on the notion that entropy is a measure of disorder, is that entropy should be positive. However, there are circumstances in which entropy can take on negative values. For example, negative entropy is often discussed in connection with biological systems [1]. More interesting physically is the occurrence of negative entropy in black-hole and cosmological physics [2,3].In Casimir physics, perhaps the first appearance of negative entropy occurred in connection with the description of the quantum vacuum interaction between parallel conducting plates. If dissipation is present, the entropy of the interaction is positive at large distances, aT ≫ 1, where a is the separation between the plates and T is the temperature, but turns negative for short distances. Considered as a function of temperature, the sign of the entropy changes as the temperature decreases, but does tend to zero as the temperature tends to zero, in accordance with the Nernst heat theorem [4]. Although perhaps surprising, this was not thought to be a problem because this phenomenon only referred to the interaction part of the free energy, and the total entropy of the system was expected to be positive. Somewhat later it was discovered that negative Casimir entropies also occurred purely geometrically, for example between a perfectly conducting sphere and a perfectly conducting plane without dissipation [5][6][7], or between two spheres [8,9]. When the distance times the temperature (in natural units) is of order unity, typically a negative entropy region was present. Since the effect was dominant in the dipole approximation, this led to a systematic study of the phenomenon of negative entropy arising between polarizable particles, characterized by electric and magnetic polarizabilities, or between such particles and a conducting plate. For appropriate choices of these polarizabilities, these nanoparticles behaved like small conducting spheres. We found that sometimes the entropy started off negatively for small aT , before eventually turning positive, and sometimes the entropy was first positive, turned negative for a while, and then turned positive again as aT increased [10,11]. The combined effects of both geometry and dissipation are considered in Refs. [12,13].The occurrence of negative entropy, geometricall...

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Negative entropies in Casimir and Casimir‐Polder interactions

Cited by 23 publications

References 25 publications

Negativity of the Casimir Self-Entropy in Spherical Geometries

Negativity of the Casimir Self-Entropy in Spherical Geometries

Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution

Casimir self-entropy of a spherical electromagnetic δ -function shell

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