Entropy fluctuations as a mixedness quantifier

We propose a mixedness quantifier based on entropy fluctuations. It provides information about the degree of mixedness either for finite dimensional and infinite dimensional Hilbert spaces. It may be used to determine the reduction of the Hilbert space as it becomes maximum when, either the state is maximally mixed, or, when the Hilbert space effectively reduces its dimensions, such as in the atom field interaction where the two-level atom dictates the final dimension of the field.