Qualms concerning Tsallis's condition of pseudo-additivity as a definition of non-extensivity

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The pseudo-additive relation that the Tsallis entropy satisfies has nothing whatsoever to do with the super- and sub- additivity properties of the entropy. The latter properties, like concavity and convexity, are couched in geometric inequalities and cannot be reduced to equalities. Rather, the pseudo-additivity relation is a functional equation that determines the functional forms of the random entropies. The Arimoto entropy satisfies a similar pseudo-additive relation and yet it is a first order homogeneous form. Hence no conclusions can be drawn on the extensive nature of the system from either the Tsallis or Arimoto entropy based on the pseudo-additive equation.
6 pages

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Statistical Mechanics

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http://salesiana.dossiersoluciones.com/handle/123456789/22732

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cond-mat/0311477
 http://arxiv.org/abs/cond-mat/0311477

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arXiv