  We consider a previously proposed non-extensive statistical mechanics in
which the entropy depends only on the probability, this was obtained from a
f(\beta) distribution and its corresponding Boltzmann factor. We show that the
first term correcting the usual entropy also arises from several f(\beta)
distributions, we also construct the corresponding H-function and demonstrate
that a generalized H-theorem is fulfilled. Furthermore, expressing this
H-function as function of the simplest Maxwellian state we find, up to a first
approximation some modified thermodynamic quantities for an ideal gas. In order
to gain some insight about the behavior of the proposed generalized statistics,
we present some simulation results for the case of a square-well and
Lennard-Jones potentials, showing that an effective repulsive interaction is
obtained with the new formalism.
