Estimate of the entropy of radiation by means of weight functions

The entropy of radiation is estimated by means of weight functions that characterize the representation of the density operator in coherent states. An upper bound is always valid and a lower bound when there is a positive $\mathscr P$-representation. A necessary condition is formulated that must be satisfied by the diagonal elements of the density operator in the population number space if the operator is to have a positive $\mathscr P$-representation.