An Extended Model of Non-Integer-Dimensional Space for Anisotropic Solids with q-Deformed Derivatives
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914472966225920 |
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| author | Weberszpil, José Metzler, Ralf |
| author_facet | Weberszpil, José Metzler, Ralf |
| contents | We propose a non-integer-dimensional spatial model for anisotropic solids by incorporating a q-deformed derivative operator, inspired by the Tsallis nonadditive entropy framework. This generalization provides an analytical framework to explore anisotropic thermal properties, within a unified and flexible mathematical formalism. We derive explicit expressions for the phonon density of states and specific heat capacity, highlighting the impact of the deformation parameter q on the thermodynamic behavior. We apply the model to various solid-state materials, achieving excellent agreement with experimental data across a wide temperature range, and demonstrating its effectiveness in capturing anisotropic and subextensive effects in real systems. Beyond providing accurate fits, we anchor the q-deformation in a microscopic disorder/kinetics exponent μemerging from conformable dynamics, thereby linking nonextensive statistics to measurable heterogeneity and memory effects. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_18127 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Extended Model of Non-Integer-Dimensional Space for Anisotropic Solids with q-Deformed Derivatives Weberszpil, José Metzler, Ralf Statistical Mechanics Materials Science Soft Condensed Matter Mathematical Physics Classical Physics We propose a non-integer-dimensional spatial model for anisotropic solids by incorporating a q-deformed derivative operator, inspired by the Tsallis nonadditive entropy framework. This generalization provides an analytical framework to explore anisotropic thermal properties, within a unified and flexible mathematical formalism. We derive explicit expressions for the phonon density of states and specific heat capacity, highlighting the impact of the deformation parameter q on the thermodynamic behavior. We apply the model to various solid-state materials, achieving excellent agreement with experimental data across a wide temperature range, and demonstrating its effectiveness in capturing anisotropic and subextensive effects in real systems. Beyond providing accurate fits, we anchor the q-deformation in a microscopic disorder/kinetics exponent μemerging from conformable dynamics, thereby linking nonextensive statistics to measurable heterogeneity and memory effects. |
| title | An Extended Model of Non-Integer-Dimensional Space for Anisotropic Solids with q-Deformed Derivatives |
| topic | Statistical Mechanics Materials Science Soft Condensed Matter Mathematical Physics Classical Physics |
| url | https://arxiv.org/abs/2506.18127 |