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

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

2003-11-20

arxiv.org/abs/cond-mat/0311477v1

Physics

Condensed Matter

Statistical Mechanics

6 pages

Scientific paper

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.

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