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José Weberszpil

Publications and source records attributed to José Weberszpil.

13 recordsLinked to original sources
arXiv2026

Entropic Time, Psychophysics, and Deformed Neural Dynamics: A Unified Physical Theory for Human Time Perception

We present a unified physical theory demonstrating that human subjective time perception does not track geometric coordinate time $t$, but instead emerges from a local metric mutation driven by macroscopic physical entropy production. By establishing the Nonextensive Troika -- a closed, mutually dependent algebraic triplet linking the phase-space fractal dimension $D$, the conformable derivative order $α$, and the Tsallis nonextensive parameter $q$ -- we eliminate independent phenomenological fitting constants. We prove that the local time metric inherently scales as $t^α$, deriving the conformable operator as a necessary kinetic consequence. Furthermore, we derive the $q$-index from the equiprobable monofractal Tsallis entropy $S_q$. This structural closure unifies anomalous neural dissipative transport within a deformed leaky integrate-and-fire framework and analytically predicts macroscopic psychophysical response transitions, providing a clear thermodynamic basis for time dilation in psychedelic states (the REBUS model) and temporal compression during cognitive aging.

physics.bio-ph↗
arXiv2026

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

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.

cond-mat.stat-mech↗
arXiv2026

Conformable Scaling and Critical Dynamics: A Unified Framework for Phase Transitions

We investigate the application of conformable derivatives to model critical phenomena near continuous phase transitions. By incorporating a deformation parameter into the differential structure, we derive unified expressions for thermodynamic observables such as heat capacity, magnetization, susceptibility, and coherence length, each exhibiting power-law behavior near the critical temperature. The conformable derivative framework naturally embeds scale invariance and critical slowing down into the dynamics without resorting to fully nonlocal fractional calculus. Modified Ginzburg-Landau equations are constructed to model superconducting transitions, leading to analytical expressions for the order parameter and London penetration depth. Experimental data from niobium confirm the model's applicability, showing excellent fits and capturing asymmetric scaling behavior around Tc. This work offers a bridge between classical mean-field theory and generalized scaling frameworks, with implications for both theoretical modeling and experimental analysis.

cond-mat.stat-mech↗
arXiv2025

Microscopic Origins of Conformable Dynamics: From Disorder to Deformation

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.

cond-mat.stat-mech↗
arXiv2024

Conformable Derivative Approach to Granular Gases

Proper modeling of complex systems requires innovative mathematical tools. In this sense, we sought to use deformed or fractal derivatives for studying the dynamics of systems, particularly those, such as granular gases, in which the description of the dynamics can be done by using the stretched exponential probability densities. In this contribution we draw up three results of this application of mathematical tools. The first result shows that when we use constraints with finite momentum and the principle of maximum entropy, the Kohlrausch--Williams--Watts function, known as stretched exponential, emerges naturally and in a simpler way, when compared to results in the literature. Next, we obtain generalized expressions for the Langevin equation, as well as its solutions for three different deformed derivatives, including those connected with nonaddictive statistical mechanics. The Haff's-like law for granular gases are obtained. Next, we calculate the partition function $Z$ for a granular gas system by building up the probability density in terms of the stretched exponential function. From this partition function, we determine the internal energy of the system as well as the specific heat, both dependent on temperature. The consistency with classical approach of kinetic theory for ideal gases was verified.

cond-mat.stat-mech↗
arXiv2020

A fractal viewpoint to COVID-19 infection

One of the central tools to control the COVID-19 pandemics is the knowledge of its spreading dynamics. Here we develop a fractal model capable of describe this dynamics, in term of daily new cases, and provide quantitative criteria for some predictions. We propose a fractal dynamical model using conformed derivative and fractal time scale. A Burr-XII shaped solution of the fractal-like equation is obtained. The model is tested using data from several countries, showing that a single function is able to describe very different shapes of the outbreak. The diverse behavior of the outbreak on those countries is presented and discussed. Moreover, a criterion to determine the existence of the pandemic peak and a expression to find the time to reach herd immunity are also obtained.

physics.soc-ph↗
arXiv2018

Dual Conformable Derivative: Definition, Simple Properties and Perspectives for Applications

In this communication, one shows that there exists in the literature a certain form of deformed derivative that can here be identified as the dual of conformable derivative. The deformed subtraction is used here, together with the duality concept, as the basic definitions and starting points in order to obtain the connected dual operators. The q-exponential, in the context of generalized statistical mechanics, is the eigenfunction of this dual conformable derivative. The basic properties of the dual deformed-derivatives and also some perspective of applications and simple models are presented. The importance of this deformed derivative for position-dependent models is highlighted. An outlook of potential applications and developments is presented.

math-ph↗
arXiv2017

Structural Derivative Model for Tissue Radiation Response

By means of a recently-proposed metric or structural derivative, called scale-q-derivative approach, we formulate differential equation that models the cell death by a radiation exposure in tumor treatments. The considered independent variable here is the absorbed radiation dose D instead of usual time. The survival factor, Fs, for radiation damaged cell obtained here is in agreement with the literature on the maximum entropy principle, as it was recently shown and also exhibits an excellent agreement with the experimental data. Moreover, the well-known linear and quadratic models are obtained. With this approach, we give a step forward and suggest other expressions for survival factors that are dependent on the complex tumor structure.

physics.med-ph↗
arXiv2017

Structural scale $q-$derivative and the LLG-Equation in a scenario with fractionality

In the present contribution, we study the Landau-Lifshitz-Gilbert equation with two versions of structural derivatives recently proposed: the scale $q-$derivative in the non-extensive statistical mechanics and the axiomatic metric derivative, which presents Mittag-Leffler functions as eigenfunctions. The use of structural derivatives aims to take into account long-range forces, possible non-manifest or hidden interactions and the dimensionality of space. Having this purpose in mind, we build up an evolution operator and a deformed version of the LLG equation. Damping in the oscillations naturally show up without an explicit Gilbert damping term.

math-ph↗
arXiv2015

Variational Approach and Deformed Derivatives

Recently, we have demonstrated that there exists a possible relationship between q-deformed algebras in two different contexts of Statistical Mechanics, namely, the Tsallis' framework and the Kaniadakis' scenario, with a local form of fractional-derivative operators for fractal media, the so-called Hausdorff derivatives, mapped into a continuous medium with a fractal measure. Here, in this paper, we present an extension of the traditional calculus of variations for systems containing deformed-derivatives embedded into the Lagrangian and the Lagrangian densities for classical and field systems. The results extend the classical Euler-Lagrange equations and the Hamiltonian formalism. The resulting dynamical equations seem to be compatible with those found in the literature, specially with mass-dependent and with nonlinear equations for systems in classical and quantum mechanics. Examples are presented to illustrate applications of the formulation. Also, the conserved Nether current, are worked out.

math-ph↗
arXiv2015

On the Zitterbewegung Transient Regime in a Coarse-Grained Space-Time

In the present contribution, by studying a fractional version of Dirac's equation for the electron, we show that the phenomenon of Zitterbewegung in a coarse-grained medium exhibits a transient oscillatory behavior, rather than a purely oscillatory regime, as it occurs in the integer case, $α=1$. Our result suggests that, in such systems, the Zitterbewegung-type term related to a trembling motion of a quasiparticle is tamed by its complex interactions with other particles and the medium. This can justify the difficulties in the observation of this interesting phenomenon. The possibility that the Zitterbewegung be accompanied by a damping factor supports the viewpoint of particle substructures in Quantum Mechanics.

hep-th↗
arXiv2012

The Fractional London Equation and The Fractional Pippard Model For Superconductors

With the discovery of new superconductors there was a running to find the justifications for the new properties found in these materials. In order to describe these new effects some theories were adapted and some others have been tried. In this work we present an application of the fractional calculus to study the superconductor in the context of London theory. Here we investigated the linear London equation modified by fractional derivatives for non-differentiable functions, instead of integer ones, in a coarse grained scenario. We apply the fractional approach based in the modified Riemann-Liouville sense to improve the model in order to include possible non-local interactions and the media. It is argued that the e ects of non-locality and long memory, intrinsic to the formalism of the fractional calculus, are relevant to achieving a satisfactory phenomenological description. In order to compare the present results with the usual London theory, we calculated the magnetic field distribution for a mesoscopic superconductor system. Also, a fractional Pippard-like model is proposed to take into account the non-locality beside effects of interactions and the media. We propose that parameter alfa of fractionality can be used to create an alternative way to characterize superconductors.

cond-mat.supr-con↗