The additive generalization of the Boltzmann entropy
Alexander N. Gorban, Iliya V. Karlin, Hans Christian Ottinger
TL;DR
This paper introduces a unique additive generalization of the Boltzmann entropy, providing analytical solutions for extended ensembles and exploring the deformation of uncorrelated states.
Contribution
It presents the only known additive one-parameter family of generalized Boltzmann entropies with analytical solutions for extended statistical ensembles.
Findings
Unique additive one-parameter family of generalized entropies
Analytical solutions for extended ensembles
Detailed analysis of uncorrelated state deformation
Abstract
There exists only one generalization of the classical Boltzmann-Gibbs-Shannon entropy functional to a one-parametric family of additive entropy functionals. We find analytical solution to the corresponding extension of the classical ensembles, and discuss in some detail the example of the deformation of the uncorrelated state.
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