A possible generalization Shannon’s entropy using q-calculus

Bouzenada Abdelmalek, A. R. P. Moreira, Rami Ahmad El-Nabulsi +2 more

Abdelmalek Bouzenada, Allan R. Moreira, Rami Ahmad El‐Nabulsi +2 more

Armin Uhlmann

Nelson Flores-Gallegos

In this report, we present three generalized expressions of Shannon’s entropy using the electron densities of position and momentum spaces. Such expressions were obtained using the definition of deformed logarithm introduced by Tsallis. We show that only one expression fulfils the dimensionless criterion, it is strictly positive overall space and follows a growing behavior with respect to the electron number. We also found that by using some values of [Formula: see text], it is possible to reproduce the general trends of the radial distribution in position space and momentum space of the neon atom.

David Ellerman

Xiang Gao, Emilio Gallicchio, Adrian E. Roitberg

We show that the generalized Boltzmann distribution is the only distribution for which the Gibbs-Shannon entropy equals the thermodynamic entropy. This result means that the thermodynamic entropy and the Gibbs-Shannon entropy are not generally equal, but rather the equality holds only in the special case where a system is in equilibrium with a reservoir.