2025/07/05 by Weberszpil, José
#Classical Physics (physics.class-ph) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Physics (math-ph) #Other Condensed Matter (cond-mat.other) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2507.04078
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 T1-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.