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Jaume Gine

Publications and source records attributed to Jaume Gine.

7 recordsLinked to original sources
arXiv2026

Quantum Gravity from Fractal Entanglement Geometry

In this paper we propose that spacetime is an emergent fractal geometry generated by the entanglement structure of an underlying quantum information network. Indeed, it is developed a framework in which spacetime, quantum mechanics, and gravity emerge from the entanglement structure of a universal quantum state. Geometry is defined by an information-theoretic distance $d_{ij}=-\ell_0\log(I_{ij}/I_0)$ on an entanglement graph, producing a scale-dependent, fractal spacetime whose effective dimension flows toward $D\to 2$ near the Planck scale. In this fractal geometry, nondifferentiable trajectories lead to stochastic geodesics and a complex covariant derivative, from which the Schr\"odinger equation follows as an emergent dynamical law. Gravity arises from the time dependence of the entanglement-induced metric, yielding Einstein gravity in the macroscopic limit and fractal corrections encoded in a generalized field equation $G_{\mu\nu}=8\pi G(T_{\mu\nu}+\alpha E_{\mu\nu}+\beta F_{\mu\nu})$. The resulting \emph{Fractal Entanglement Quantum Gravity} (FEQG) framework predicts dimensional reduction, modified gravitational potentials, and possible deviations from standard quantum mechanics at ultrashort scales, offering a unified informational origin for quantum theory and gravitation.

gr-qc↗
arXiv2026

On the Possibility of Quantum Gravity Emerging from Geometry

Can the generalized uncertainty principle (GUP) arise as an effective manifestation of spacetime geometry rather than as a fundamental postulate? More specifically, can the gravitational GUP be interpreted as an emergent uncertainty relation generated by the statistical microstructure of local horizons? Motivated by these questions, this work explores the broader possibility that selected features of quantum-gravitational behavior may originate from the geometric and thermodynamic properties of spacetime itself. We argue that, under suitable assumptions regarding the multifractal structure of microscopic horizons, an effective GUP can indeed be induced by geometry. This perspective suggests that quantum uncertainty may be viewed not as a fundamental ingredient of nature, but as an emergent consequence of the statistical organization of spacetime at the Planck scale. While the present framework does not constitute a complete theory of quantum gravity, nor does it derive the full formalism of quantum mechanics, it provides a proof of concept for a geometric origin of generalized uncertainty relations and establishes a thermodynamic route connecting horizon microstructure, entropy corrections, and effective quantum behavior. The resulting framework is compatible with several modern approaches to quantum gravity through the common notion of scale-dependent geometry, while yielding a unified geometric interpretation of generalized uncertainty relations.

gr-qc↗
arXiv2022

Time-reversibility and integrability of p:-q resonant vector fields

We study local analytical integrability in a neighborhood of $p:-q$ resonant singular point of a two-dimensional vector field and its connection to time-reversibility with respect to the non-smooth involution $ φ(x,y)=(y^{p/q},x^{q/p}). $ Some generalizations of the theory developed by K.~S.~Sibirsky for $1:-1$ resonant case to the $p:-q$ resonant case are presented.

math.DS↗
arXiv2022

Baryogenesis in non-extensive Tsallis Cosmology

Non-extensive Tsallis thermostatistics is a widespread paradigm to describe large-scale gravitational systems. In this work we use Tsallis Cosmology to study thermodynamic gravity and derive modified Friedmann equations. We show that corrections induced by non-extensivity affect the Hubble function evolution during the radiation-dominated epoch. In turn, this leads to non-trivial modifications of the mass density and pressure content of the Universe, which provide a viable mechanism allowing for baryogenesis, even in the presence of the standard interaction between the Ricci scalar and baryon current. By demanding consistency with current observational bounds on baryogenesis, we constrain Tsallis $\delta$ parameter to be $|\delta-1| \simeq 10^{-3}$. Based on the recently established connection between Tsallis thermostatistics and the quantum gravitational generalization of the uncertainty principle at Planck scale (GUP), we finally show that this bound is in agreement with the estimation of the GUP parameter predicted by many quantum gravity models.

gr-qc↗
arXiv2009

On the cyclicity of weight-homogeneous centers

Let W be a weight-homogeneous planar polynomial differential system with a center. We find an upper bound of the number of limit cycles which bifurcate from the period annulus of W under a generic polynomial perturbation. We apply this result to a particular family of planar polynomial systems having a nilpotent center without meromorphic first integral.

math.DS↗
arXiv2007

Linearizable ordinary differential equations

Our purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be constructed by means of the solutions of linear differential equations. We give several families of differential systems which illustrate how the integrability of the system passes through the solutions of a linear differential equation. At the end of the work, we describe some families of differential systems which are Darboux integrable and whose inverse integrating factor is constructed using the solutions of a second--order linear differential equation defining a family of orthogonal polynomials.

math.DS↗