Large Deviation Theory for Bose Gas of Photons and Planck's Oscillators

TL;DR

This paper applies large deviation theory to analyze the probability distributions of photons and Planck's oscillators, reproducing classical results within a probabilistic framework and providing detailed insights into their spatial and energy distributions.

Contribution

It introduces a novel application of large deviation theorems to Bose gases, connecting classical thermodynamic results with probabilistic large deviation principles.

Findings

Calculated large deviation probabilities, entropies, and rate functions for photon and oscillator distributions.

Reproduced classical Bose and Planck results using large deviation theory.

Provided a probabilistic perspective on spatial and energy distributions in Bose gases.

Abstract

We utilize large deviation theorems to analyze the distributions of a Bose gas of photons and Planck's identical linear oscillators. By applying the Boltzmann-Sanov and Cram\'er-Chernoff theorems, we calculate the large deviation probabilities, entropies, and rate functions for the spatial and energy distributions of both photons and Planck's oscillators. Our study reproduces the results of Bose and Planck within the framework of large deviation theory.