Plastino, Angel R.; Constantino Tsallis; Roseli S. Wedemann and Hans J. Haubold
Several generalizations or extensions of the Boltzmann–Gibbs thermostatistics, based on non-standard entropies, have been the focus of considerable research activity in recent years. Among these, the power-law, non-additive entropies ?? ≡ ?1−∑?????−1 (? ∈ ℝ; ?1 = ??? ≡ −? ∑? ?? ln ??) features of the ?? thermostatistics, therefore, are worthy of close scrutiny. In the present work, we analyze one of these features, according to which the q-logarithm function ln? ? ≡ ?1 − ? − 11 −? (ln1 ? = ln?) associated with the ?? entropy is linked, via a duality relation, to the q-exponential function characterizing the maximum-entropy probability distributions. We enquire into which entropic functionals lead to this or similar structures, and investigate the co