Abstract
The existence and exact form of the continuum expression of the discrete nonlogarithmic -entropy is an important open problem in generalized thermostatistics, since its possible lack implies that nonlogarithmic -entropy is irrelevant for the continuous classical systems. In this work, we show how the discrete nonlogarithmic -entropy in fact converges in the continuous limit and the negative of the -entropy with continuous variables is demonstrated to lead to the (Csiszár type) -relative entropy just as the relation between the continuous Boltzmann-Gibbs expression and the Kullback-Leibler relative entropy. As a result, we conclude that there is no obstacle for the applicability of the -entropy to the continuous classical physical systems.
- Received 20 September 2017
DOI:https://doi.org/10.1103/PhysRevE.97.012104
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