Logical entropy and negative probabilities in quantum mechanics

The concept of Logical Entropy, S L = 1-? n i =1 p 2 , where the are normalized probabilities, was introduced by David Ellerman in a series recent papers. Although mathematical formula itself is not new, provided sound probabilistic interpretation as measure distinctions partition on given set. same comes across useful definition entropy quantum mechanics, it linked to notion purity state. quadratic form logical lends generalization probabilities that include negative values, an idea goes back Feynman and Wigner. Here, we analyze reinterpret light entropy. Several intriguing quantum-like properties derived discussed finite dimensional spaces. For infinite-dimensional spaces (continuum), show that, under sole hypothesis total probability preserved time, one obtains evolution equation for density basically identical Wigner function phase space, at least when considers only momentum variable. This result suggest plays profound role establishing peculiar rules physics.