Statistics of classical blackbody radiation with ground state

A classical model of blackbody radiation is investigated in which the field is produced by N_T incoherent thermal sources and N₀ incoherent sources of a ground state with Lorentz-invariant spectral energy density proportional to the frequency ω. Bundles of 2N nearly monochromatic, nearly parallel cavity modes are considered, and general formulas for all moments of the energy density ${\rho }_b$ and the energy $H_b$ in a bundle are derived by the use of the central limit theorem. It is found that the energy H of one cavity mode is a fluctuating quantity because of interference of the field contributions from different sources. This causes an energy distribution $W\left(H\right)={〈H〉}^{-1}exp(-\frac{H}{〈H〉})$ which is formally different from the canonical energy distribution. The moments 〈H^q〉 obtained from W(H) agree with those obtained by quantum statistics for q=1 and q=2, but disagree for q>2; the higher moments are also inconsistent with some general relations of the canonical ensemble theory. Suggestions are made for achieving full equivalence between the classical model and quantized blackbody radiation.