Nonlocal impedances and the Casimir entropy at low temperatures

Abstract

The problem with the temperature dependence of the Casimir force is investigated. Specifically, the entropy behavior in the low temperature limit, which caused debates in the literature, is analyzed. It is stressed that the behavior of the relaxation frequency in the T-->0 limit does not play a physical role since the anomalous skin effect dominates in this range. In contrast with the previous works, where the approximate Leontovich impedance was used for analysis of nonlocal effects, we give description of the problem in terms of exact nonlocal impedances. It is found that the Casimir entropy is going to zero at T-->0 only in the case when s polarization does not contribute to the classical part of the Casimir force. However, the entropy approaching zero from the negative side that, in our opinion, cannot be considered as thermodynamically satisfactory. The resolution of the negative entropy problem proposed in the literature is analyzed and it is shown that it cannot be considered as complete. The crisis with the thermal Casimir effect is stressed.

Geometric origin of negative Casimir entropies: A scattering-channel analysis

“…Furthermore, in the large-distance limit the matrix elements of the roundtrip operator are very small and we may expand the logarithm in (7). In view of tr(A) = log[det(exp(A))] with tr denoting the trace, we then obtain…”

“…During the last decade or so various papers have focused on the entropy related to the Casimir interactions between two solid bodies [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. An important reason for this interest lies in the fact that the Casimir entropy can reach negative values.…”

Temperature dependence of the magnetic Casimir-Polder interaction

“…The behavior seen in the previous figures indicates significantly different entropies for the surface models, with a strong dependence on the presence of dissipation (conductivity) at low frequencies. This parallels the discussion of the macroscopic Casimir entropy for the dispersion interaction between two plates, a subject of recent controversies, where the Drude and plasma models give different answers [43,[63][64][65][66][67]. The results that follow indicate that the magnetic Casimir-Polder interaction may provide an alternative scenario to investigate this point.…”

“…[65,66] it has been shown that not only dissipation but also nonlocality of the response has strong implications for the entropy. In particular, the residual entropy ∆S = 0 vanishes, because at very low temperatures, the anomalous skin effect and Landau damping take the role of a nonzero dissipation rate.…”

Reply to “Comment on ‘Analytical and numerical verification of the Nernst theorem for metals’ ”

“…It should be noted that on the molecular level the permittivity becomes non-local, ε = ε(ω, k), where k is the magnitude of the wave vector k. Then ε becomes finite for finite k. Only the special case ε(0, 0) is infinite, and this ("measure zero") can not be expected to give a finite contribution to the Casimir force. In independent studies Svetovoy and Esquivel [6] and Sernelius [7] find that the TE zero mode should not contribute when spatial dispersion is carefully taken into account. Because of nonlocal effects, the former of these state, "the question does [ν] go to zero or have some residual value at T → 0 becomes unimportant" and they find that the TE zero frequency contribution must indeed be zero to satisfy Nernst's theorem.…”