On the uniqueness theorem for pseudo-additive entropies
Mathematical Physics
2017-11-15 v1 Statistical Mechanics
math.MP
Abstract
We discuss the idea that the Tsallis-type (q-additive) entropic chain rule allows for a wider class of entropic functionals than previously thought. In particular, we point out that the ensuing entropy solutions (e.g., Tsallis entropy) can be determined uniquely only when one fixes the prescription for handling conditional entropies. Our point is substantiated with the Dar\'otzy's mapping theorem and DeFinetti-Kolmogorov theorem for escort distributions and illustrated with a number of examples. Connection with Landsberg's classification of non-extensive thermodynamical systems is also briefly discussed.
Keywords
Cite
@article{arxiv.1709.06359,
title = {On the uniqueness theorem for pseudo-additive entropies},
author = {Petr Jizba and Jan Korbel},
journal= {arXiv preprint arXiv:1709.06359},
year = {2017}
}