Generalizing Planck's distribution by using the Carati-Galgani model of molecular collisions

TL;DR

This paper generalizes Planck's distribution by incorporating Lévý-type energy exchange statistics in classical harmonic oscillator systems, linking classical and quantum statistical mechanics through a nonextensive framework.

Contribution

It introduces a novel generalization of Planck's law using the Carati-Galgani model and nonextensive statistical mechanics, bridging classical and quantum descriptions.

Findings

The generalized distribution aligns with nonextensive statistical mechanics.

Energy exchanges follow Lévý-type statistics in the model.

Compatibility with quantum statistical mechanics relations.

Abstract

Classical systems of coupled harmonic oscillators are studied using the Carati-Galgani model. We investigate the consequences for Einstein's conjecture by considering that the exchanges of energy, in molecular collisions, follows the L\'evy type statistics. We develop a generalization of Planck's distribution admitting that there are analogous relations in the equilibrium quantum statistical mechanics of the relations found using the nonequilibrium classical statistical mechanics approach. The generalization of Planck's law based on the nonextensive statistical mechanics formalism is compatible with the our analysis.