Microscopic Origins of Conformable Dynamics: From Disorder to Deformation
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911041208713216 |
|---|---|
| author | Weberszpil, José |
| author_facet | Weberszpil, José |
| contents | Conformable derivatives have attracted increasing interest for bridging classical and fractional calculus while retaining analytical tractability. However, their physical foundations remain underexplored. In this work, we provide a systematic derivation of conformable relaxation dynamics from microscopic principles. Starting from a spatially-resolved Ginzburg-Landau framework with quenched disorder and temperature-dependent kinetic coefficients, we demonstrate how spatial heterogeneity and energy barrier distributions give rise to emergent power-law memory kernels. In the adiabatic limit, these kernels reduce to a conformable temporal structure of the form T^{1-μ}\,dψ/dT. The deformation parameter μis shown to be connected to experimentally measurable properties such as transport coefficients, disorder statistics, and relaxation time spectra. This formulation also reveals a natural link with nonextensive thermodynamics and Tsallis entropy. By unifying memory effects, anomalous relaxation, and spatial correlations under a coherent physical mechanism, our framework transforms conformable derivatives from heuristic tools into physically grounded operators suitable for modeling complex critical dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Microscopic Origins of Conformable Dynamics: From Disorder to Deformation Weberszpil, José Statistical Mechanics Disordered Systems and Neural Networks Other Condensed Matter Mathematical Physics Classical Physics Conformable derivatives have attracted increasing interest for bridging classical and fractional calculus while retaining analytical tractability. However, their physical foundations remain underexplored. In this work, we provide a systematic derivation of conformable relaxation dynamics from microscopic principles. Starting from a spatially-resolved Ginzburg-Landau framework with quenched disorder and temperature-dependent kinetic coefficients, we demonstrate how spatial heterogeneity and energy barrier distributions give rise to emergent power-law memory kernels. In the adiabatic limit, these kernels reduce to a conformable temporal structure of the form T^{1-μ}\,dψ/dT. The deformation parameter μis shown to be connected to experimentally measurable properties such as transport coefficients, disorder statistics, and relaxation time spectra. This formulation also reveals a natural link with nonextensive thermodynamics and Tsallis entropy. By unifying memory effects, anomalous relaxation, and spatial correlations under a coherent physical mechanism, our framework transforms conformable derivatives from heuristic tools into physically grounded operators suitable for modeling complex critical dynamics. |
| title | Microscopic Origins of Conformable Dynamics: From Disorder to Deformation |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Other Condensed Matter Mathematical Physics Classical Physics |
| url | https://arxiv.org/abs/2507.04078 |