Long-range interactions, doubling measures and Tsallis entropy

Abstract

We present a path toward determining the statistical origin of the thermodynamic limit for systems with long-range interactions. We assume throughout that the systems under consideration have thermodynamic properties given by the Tsallis entropy. We rely on the composition property of the Tsallis entropy for determining effective metrics and measures on their configuration/phase spaces. We point out the significance of Muckenhoupt weights, of doubling measures and of doubling measure-induced metric deformations of the metric. We comment on the volume deformations induced by the Tsallis entropy composition and on the significance of functional spaces for these constructions.

26 pages, No figures, Standard LaTeX. Revised version: addition of a paragraph on a contentious issue (Sect. 3). To be published by Eur. Phys. J. B

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Cited by in corpus (11)

• Ricci curvature, isoperimetry and a non-additive entropy
• Entropies from coarse-graining: convex polytopes vs. ellipsoids
• Analysis of Tsallis' classical partition function's poles
• Rescuing the MaxEnt treatment for $q$-generalized entropies
• Moduli of curve families and (quasi-)conformality of power-law entropies
• Irreversibility from staircases in symplectic embeddings
• Hidden correlations entailed by q-non additivity render the q-monoatomic gas highly non trivial
• Verlinde's emergent gravity in an $\mathbf{n}-$dimensional, non-additive Tsallis' scenario
• Physical peculiarities of divergences emerging in q-deformed statistics
• q-Path entropy phenomenology for phase-space curves
• The ${\tau }_q$-Fourier transform: covariance and uniqueness