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 tL, at which both laws are simultaneously satisfied. Strikingly, classical spectra obtained for different energies and cavity sizes collapse onto the universal Planck distribution at tL. We conjecture that quantum dynamical localization arrests the classical energy cascade at tL, and that the Planck distribution emerges as a dynamical consequence of this arrest - without invoking any a priori statistical assumption.
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BibTeX
@misc{wang2026classicaltoquantum,
title = {{Classical-to-Quantum Transition in Blackbody Radiation Thermodynamics: Planck's Law without Statistical Assumptions}},
author = {J. Wang and G. Casati and G. Benenti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27858},
eprint = {2610.27858},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27858},
}
RIS
TY - UNPB
TI - Classical-to-Quantum Transition in Blackbody Radiation Thermodynamics: Planck's Law without Statistical Assumptions
AU - J. Wang
AU - G. Casati
AU - G. Benenti
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27858
UR - https://arxiv.org/abs/2610.27858
AB - 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.
ER -