Product probability property, known in the literature as statistical independence, is examined first. Then generalized entropies are introduced, all of which give generalizations to Shannon entropy. It is shown that the nature of the recursivity postulate automatically determines the logarithmic...

It seems reasonable to consider concavity (with regard to all probability distributions) and stability (under arbitrarily small deformations of any given probability distribution) as necessary for an entropic form to be a physical one in the thermostatistical sense. Most known entropic forms,...

We show an interesting connection between non-standard (non-Boltzmannian) distribution functions arising in the theory of violent relaxation for collisionless stellar systems [D. Lynden-Bell, Mon. Not. R. Astron. Soc. 136 (1967) 101.] and the notion of superstatistics recently introduced by...