Properties of the “non-extensive Gaussian” entropy

The present work investigates the Lesche stability (experimental robustness), the thermodynamic stability, the Legendre structure of thermodynamics, and derives the maximum entropy distribution of the one-parametric “non-extensive Gaussian” entropy. We show that this entropy definition fulfills both stability conditions for all values of its parameter (q∈R). The entropy maximizer contains the Lambert W-function, which allows the preservation of the Legendre transformations.