Almost additive entropy
Abstract
We explore consequences of a hyperbolic metric induced by the composition property of the Harvda-Charvat/Dar\'oczy/Cressie-Read/Tsallis entropy. We address the special case of systems described by small deviations of the non-extensive parameter \ q≈ 1 \ from the "ordinary" additive case which is described by the Boltzmann/Gibbs/Shannon entropy. By applying the Gromov/Ruh theorem for almost flat manifolds, we show that such systems have a power-law rate of expansion of their configuration/phase space volume. We explore the possible physical significance of some geometric and topological results of this approach.
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