Thermodynamic q-Distributions That Aren't

TL;DR

This paper explores the properties of bosonic q-oscillators, demonstrating that their equilibrium distribution remains Planckian despite q-dependent emission and absorption rates, and discusses implications for black-body radiation and maximum cavity size.

Contribution

It clarifies that q-oscillators do not alter the fundamental Planck distribution and addresses misconceptions about q-deformations in black-body radiation.

Findings

Q-oscillators maintain Planck distribution despite q-dependent rates

A maximum cavity size or temperature is suggested based on emission/absorption rates

Discussion clarifies misconceptions about q-oscillations in black-body radiation

Abstract

Bosonic q-oscillators commute with themselves and so their free distribution is Planckian. In a cavity, their emission and absorption rates may grow or shrink---and even diverge---but they nevertheless balance to yield the Planck distribution via Einstein's equilibrium method, (a careless application of which might produce spurious q-dependent distribution functions). This drives home the point that the black-body energy distribution is not a handle for distinguishing q-excitations from plain oscillators. A maximum cavity size is suggested by the inverse critical frequency of such emission/absorption rates at a given temperature, or a maximum temperature at a given frequency. To remedy fragmentation of opinion on the subject, we provide some discussion, context, and references.