Another physical expression of the entropy for an ideal photon gas

• Published in: Chemical physics 2019-06, Vol.522, p.55-58
• Main Author: Nagata, Shoichi
• Format: Article
• Language: English
• Subjects: Fluctuation analysis; Heisenberg uncertainty relation; Photon gas entropy formula; Planck’s black-body entropy; Thermal uncertainty relation
• ISSN: 0301-0104
• DOI: 10.1016/j.chemphys.2019.02.001

Entropy of an ideal photon gas as a function of thermal uncertainty. The entropy is in direct proportion to the magnitude of the uncertainty ΔxTΔpxT/h3. [Display omitted] •An alternative expression to entropy formula for an ideal photon gas is provided.•A thermal uncertainty relation for a photon gas is introduced and obtained.•The ideal photon gas entropy is given in terms of the thermal uncertainty relation.•A comparative study of entropy, between massless photon gas and classical ideal gas with a mass, is presented.•The entropy of photon gas reflects the Heisenberg uncertainty relation in quantum state. An expression of the entropy for massless photon gas in a unit volume is provided. A quantity, (Δx)T(Δpx)T, is introduced, which indicates the magnitude of an average uncertainty at certain temperature T. The entropy of the photon gas can be written in terms of thermal uncertainty (Δx)T(Δpx)T. The analytical derivation is carried out on the basis of fluctuation theory, for a canonical system in thermal equilibrium at T. The emphasis is given to the intimate connection between the uncertainty in the quantum mechanics and the entropy in macroscopic world. This new entropy formula of a zero mass m=0 ideal photon gas is discussed in comparison with that of a mass particle (m≠0) ideal gas.