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Extended model of noninteger-dimensional space for anisotropic solids with q-deformed derivatives

José Weberszpil1,* and Ralf Metzler2,†

  • *Contact author: josewebe@gmail.com
  • †Contact author: ralf.metzler@uni-potsdam.de
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Phys. Rev. E 114, 024137 – Published 18 August, 2026

DOI: https://doi.org/10.1103/m98w-77xg

Abstract

We propose a noninteger-dimensional spatial model for anisotropic solids incorporating a q-deformed derivative operator inspired by the Tsallis nonadditive entropy framework. This generalization provides a unified and flexible analytical formalism for exploring anisotropic thermal properties. We derive explicit expressions for the electronic and phonon densities of states and for the phonon specific heat, showing how the Hausdorff dimension α and the deformation parameter q affect the spectral and thermodynamic response. The model is applied to several solid-state materials and provides a close description of their measured specific-heat behavior over broad temperature ranges. The fitted results illustrate the ability of the regularized entropic formulation to describe departures from the standard Debye response. Finally, we relate the q-deformation qualitatively to disorder-controlled conformable kinetics, suggesting a possible connection to microscopic heterogeneity and effective memory signatures without assuming a universal quantitative relation between q and the kinetic exponent μ.

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Phys. Rev. E 114, 024137– Published 18 August, 2026
  • Received 14 April 2026
  • Accepted 30 July 2026
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