🔢 Category

math-ph

3366 papers

Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.

On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.

🔢 mathematics

Bridging Classical and Quantum Information Scrambling with the Operator Entanglement Spectrum

This paper demonstrates that the operator entanglement spectrum serves as a powerful diagnostic tool to distinguish between classical reversible automaton dynamics and fully quantum chaotic dynamics, revealing that the former follows Bernoulli random matrix statistics while the latter follows Gaussian statistics, and showing that introducing a constant number of superposition-generating gates is sufficient to drive automaton circuits into the universal random-circuit chaos class.

Ben T. McDonough, Claudio Chamon, Justin H. Wilson, Thomas Iadecola2026-03-11
🔢 mathematics

Brackets in multicontact geometry and multisymplectization

This paper introduces a graded bracket of forms on multicontact manifolds that satisfies a graded Jacobi identity and Leibniz rules, utilizes multisymplectization to connect these structures to multisymplectic geometry for deriving field equations, and applies these findings to analyze observable evolution, dissipation phenomena, and classical dissipative field theories.

Manuel de León, Rubén Izquierdo-López, Xavier Rivas2026-03-11
🔢 mathematics

Singularity of the axisymmetric stagnation-point-like solution within a cylinder of the 3D Euler incompressible fluid equations

This paper analytically demonstrates that the formation of finite-time singularities in axisymmetric 3D incompressible Euler flows within a cylinder is determined exclusively by the local geometric flatness of the initial vortex stretching rate near its global minimum, with specific power-law thresholds distinguishing between regular solutions and blowup scenarios depending on the singularity's location.

Yinshen Xu, Miguel D. Bustamante2026-03-11
🔢 mathematics

On the Mathematical Analysis and Physical Implications of the Principle of Minimum Pressure Gradient

This paper establishes a rigorous two-way equivalence between the incompressible Navier-Stokes equations and the principle of minimum pressure gradient (PMPG), demonstrating that the former is mathematically identical to the instantaneous minimization of the pressure force required to enforce incompressibility, thereby offering a variational framework that generalizes classical Galerkin projections and provides new insights into flow stability and the vanishing-viscosity limit.

Haithem Taha2026-03-11