Thermodynamics of a quantized electromagnetic field in absorbing media

Because induced emission is an incoherent phenomenon, it is impossible to represent the Gibbs thermodynamic potential of a quantized electromagnetic field in an absorbing medium in terms of the standard refractive index with an imaginary component. This is completely true with respect to the entropy of the electromagnetic field, the heat capacity, and the state equation, as well as to the stationary ponderomotive forces. The so-called causal refractive index arises in the theory, which differs from the standard refractive index in the analytical properties. The ideality condition of the photon gas in dissipative media does not hold without using the causal refractive index. The Kirchhoff law holds true only if the causal refractive index negligibly differs from unity.