Another physical expression of the entropy for an ideal photon gas

Abstract An expression of the entropy for massless photon gas in a unit volume is provided. A quantity, ( Δ x ) T ( Δ p x ) 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 ( Δ x ) T ( Δ p x ) 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.