Complete Quantum Thermodynamics of the Black Body Photon Gas

TL;DR

This paper demonstrates that the complete quantum thermodynamics of black body photon gas can be achieved using simple thermodynamic methods without relying on quantum statistical distributions, providing practical and accurate parameter calculations.

Contribution

It introduces a non-statistical quantum thermodynamic approach to fully describe black body photon gas, bypassing traditional quantum statistical methods.

Findings

Parameters and variables can be obtained with few percent error

A quantum thermodynamic stability condition is established

Conceptual links between photon gas entropy and black hole entropy are discussed

Abstract

Kelly and Leff demonstrated and discussed formal and conceptual similarities between basic thermodynamic formulas for the classical ideal gas and black body photon gas. Leff pointed out that thermodynamic formulas for the photon gas cannot be deduced completely by thermodynamic methods since these formulas hold two characteristic parameters, {\it r} and {\it b}, whose accurate values can be obtained exclusively by accurate methods of the quantum statistics (by explicit use of the Planck's or Bose-Einstein distribution). In this work we prove that the complete quantum thermodynamics of the black body photon gas can be done by simple, thermodynamic (non-statistical) methods. We prove that both mentioned parameters and corresponding variables (photons number and pressure) can be obtained very simply and practically exactly (with relative error about few percent), by non-statistical (without any use of the Planck's or Bose-Einstein distribution), quantum thermodynamic methods. Corner-stone of these methods represents a quantum thermodynamic stability condition that is, in some degree, very similar to quantum stability condition in the Bohr quantum atomic theory (de Broglie's interpretation of the Bohr quantization postulate). Finally, we discuss conceptual similarities between black body photon gas entropy and Bekenstein-Hawking black hole entropy.