Classical-to-Quantum Transition in Blackbody Radiation Thermodynamics: Planck's Law without Statistical Assumptions

Abstract

Inspired by Fermi's model of radiation-matter interaction, we investigate the classical dynamics of a closed, finite-energy system, in which matter is coupled to an electromagnetic field. We find that energy is progressively transferred to increasingly high-frequency field modes, so that the effective temperature of both matter and radiation approaches zero in the long-time limit - in sharp contradiction with the finite-temperature equilibrium assumed by classical blackbody thermodynamics. Requiring consistency with the Stefan-Boltzmann and Wien laws identifies a characteristic time $t_L$, at which both laws are simultaneously satisfied. Strikingly, classical spectra obtained for different energies and cavity sizes collapse onto the universal Planck distribution at $t_L$. We conjecture that quantum dynamical localization arrests the classical energy cascade at $t_L$, and that the Planck distribution emerges as a dynamical consequence of this arrest - without invoking any a priori statistical assumption.