Nilpotence in Physics: the case of Tsallis entropy

Abstract

In an attempt to understand the Tsallis entropy composition property, we construct an embedding of the reals into the set of $3\times 3$ upper triangular matrices with real entries. We explore consequences of this embedding and of the geometry of the ambient $3\times 3$ Heisenberg group. This approach establishes the polynomial growth of the volume of phase space of systems described by the Tsallis entropy and provides a general framework for understanding Abe's formula in terms of the Pansu derivative between Riemannian spaces.

4 pages. No figures. Presented by the second author at IC-MSQUARE 2012 (Budapest, Hungary, 3-7 September 2012). To appear in the IC-MSQUARE 2012 Proceedings

References in corpus (6)

• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Central limit behavior of deterministic dynamical systems
• Distributivity and deformation of the reals from Tsallis entropy
• Tsallis entropy induced metrics and CAT(k) spaces
• Vanishing largest Lyapunov exponent and Tsallis entropy
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Cited by in corpus (2)

• Long-range interactions, doubling measures and Tsallis entropy
• Generalized diffusion and asymptotics induced by Tsallis entropy