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

TL;DR

This paper investigates the negative Casimir self-entropy of nanoparticles, interpreting it as an interaction entropy and analyzing its physical origin through models of spherical particles at low temperature.

Contribution

It introduces a method to compute Casimir self-entropy of nanoparticles using polarizabilities and models, clarifying the physical meaning of negative entropies as interaction effects.

Findings

Negative self-entropy can be understood as an interaction entropy.

Vacuum entropy remains positive and dominates total entropy.

Results agree with known low-temperature limits for small particles.

Abstract

Not only are Casimir interaction entropies not guaranteed to be positive, but also, more strikingly, Casimir self-entropies of bodies can be negative. Here, we attempt to interpret the physical origin and meaning of these negative self-entropies by investigating the Casimir self-entropy of a neutral spherical nanoparticle. After extracting the polarizabilities of such a particle by examining the asymptotic behavior of the scattering Green's function, we compute the corresponding free energy and entropy. Two models for the nanoparticle, namely a spherical plasma $\delta$-function shell and a homogeneous dielectric/diamagnetic ball, are considered at low temperature, because that is all that can be revealed from a nanoparticle perspective. The second model includes a contribution to the entropy from the bulk free energy, referring to the situation where the medium inside or outside the ball fills all space, which must be subtracted on physical grounds in order to maintain consistency with van der Waals interactions, corresponding to the self-entropy of each bulk. (The van der Waals calculation is described in Appendix A.) The entropies so calculated agree with known results in the low-temperature limit, appropriate for a small particle, and are negative. But we suggest that the negative self-entropy is simply an interaction entropy, the difference between the total entropy and the blackbody entropy of the two bulks, outside or inside of the nanosphere. The vacuum entropy is always positive and overwhelms the interaction entropy. Thus the interaction entropy can be negative, without contradicting the principles of statistical thermodynamics. Because the entropy of blackbody radiation by itself plays an important role, it is also discussed, including dispersive effects, in detail.