Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation

TL;DR

This paper demonstrates that the Planck spectrum with zero-point radiation naturally maximizes entropy in a system of conducting boxes, using Casimir energies and zero-point radiation, providing a thermodynamic foundation for blackbody radiation.

Contribution

It introduces a maximum-entropy principle involving Casimir energies and zero-point radiation that uniquely derives the Planck spectrum.

Findings

Planck spectrum satisfies a natural maximum-entropy principle

Zero-point radiation and Casimir energies are integral to the analysis

The approach is demonstrated in a one-dimensional wave system

Abstract

By numerical calculation, the Planck spectrum with zero-point radiation is shown to satisfy a natural maximum-entropy principle whereas alternative choices of spectra do not. Specifically, if we consider a set of conducting-walled boxes, each with a partition placed at a different location in the box, so that across the collection of boxes the partitions are uniformly spaced across the volume, then the Planck spectrum correspond to that spectrum of random radiation (having constant energy kT per normal mode at low frequencies and zero-point energy (1/2)hw per normal mode at high frequencies) which gives maximum uniformity across the collection of boxes for the radiation energy per box. The analysis involves Casimir energies and zero-point radiation which do not usually appear in thermodynamic analyses. For simplicity, the analysis is presented for waves in one space dimension.