Probability distributions and associated nonlinear Fokker-Planck equation for the two-index entropic form S(q,δ)

The probability distributions and associated Fokker-Planck equation of the recently postulated entropic form, S(q,δ), are investigated. This entropy was proposed as an unification of the well-known S(q) of nonextensive-statistical mechanics and S(δ), which appeared lately as a possibly appropriate candidate for the black-hole entropy. The connection between S(q,δ) and a nonlinear Fokker-Planck equation, such as to satisfy an H-theorem, is explored. The stationary-state probability distribution follows a transcendental equation, which is solved numerically for typical values of q and δ. The same transcendental equation is obtained through the maximum-entropy principle, showing that the two procedures are equivalent.