Entropy of generalized Gaussian optical fields

We consider two definitions of entropy: thermodynamic entropy and signal entropy. We compare their value for the class of generalized Gaussian fields. The first definition is well adapted to monomode stationary fields, while the second one is bounded only for multimode fields. We prove that these two notions are definitely different, for example, the real Gaussian field has a maximum signal entropy and a minimum thermodynamic entropy (among the Gaussian fields).