# An Extended Model of Non-Integer-Dimensional Space for Anisotropic Solids with q-Deformed Derivatives

Source: [An Extended Model of Non-Integer-Dimensional Space for Anisotropic Solids with q-Deformed Derivatives](<https://www.sota2.com/research/paper/68fa4aa81e209131ce940143>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-04-17T05:00:04.440Z

Authors: Jos\\'e Weberszpil, Ralf Metzler

Published: 2025-06-22T18:24:22.000Z

## Abstract

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 \\mu emerging from conformable dynamics, thereby linking nonextensive statistics to measurable heterogeneity and memory effects.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2506.18127>)

[PDF](<https://arxiv.org/pdf/2506.18127.pdf>)