Density matrix and entropies for electromagnetic fields

A ‘‘window’’ concept, used previously in a phase-space representation, is extended to an energy representation. The new definition of trace is used to evaluate the properties of the density matrix and the entropy for electromagnetic fields. It is shown that the ‘‘ensemble’’ entropy behaves more closely to the ‘‘thermodynamic’’ entropy than the ‘‘physical’’ one. The source of negative entropy values is clearly shown as being due to higher contributions of virtual states.