🔢 Category

math-ph

1677 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.

Classifying fusion rules of anyons or SymTFTs: A general algebraic formula for domain wall problems and quantum phase transitions

This paper proposes a general algebraic formula based on ring homomorphisms and the Verlinde formula to classify anyon transformations across domain walls, thereby unifying the description of topological phase transitions, massless renormalization group flows, and symmetry-enriched topological orders within the framework of Symmetry Topological Field Theories (SymTFTs).

Yoshiki Fukusumi2026-04-02🔢 math-ph

Thermodynamics of dynamical black holes beyond perturbation theory

This paper resolves the thermodynamic limitations of event horizons by demonstrating that quasi-local horizons allow for a robust formulation of the first and second laws of black hole mechanics applicable to dynamical black holes arbitrarily far from equilibrium, thereby identifying black hole entropy with the area of marginally trapped surfaces rather than the event horizon.

Abhay Ashtekar, Daniel E. Paraizo, Jonathan Shu2026-04-02⚛️ gr-qc

Gradient systems and asymmetric relaxations in view of Riemannian geometry

This paper extends the relationship between gradient flows and pregeodesics from dually flat manifolds to general Riemannian manifolds by utilizing non-metricity tensors to compare relaxation rates, thereby providing a geometric explanation for the universal asymmetry where warming up is faster than cooling down in Gaussian chains.

Alessandro Bravetti, Miguel Ángel García Ariza, José Roberto Romero-Arias2026-04-02🔢 math-ph

Local Rank-One Logarithmic Instability for the Mixed Hessian of the Dispersionless Toda τ\tau-Function

This paper establishes a local rank-one logarithmic instability in the mixed Hessian of the dispersionless Toda τ\tau-function for polynomial conformal maps, demonstrating that along a subcritical path approaching a critical point, exactly one variational eigenvalue diverges logarithmically while all others remain bounded, thereby isolating the mechanism responsible for the first spectral transition preceding geometric breakdown in Laplacian growth.

Oleg Alekseev2026-04-02🔢 math-ph

Dissipation-assisted stabilization of periodic orbits via actuated exterior impacts in hybrid mechanical systems with symmetry

This paper demonstrates that while actuated exterior impacts alone cannot stabilize periodic orbits in symmetric hybrid mechanical systems like the pendulum-on-a-cart, the combination of such impacts with dissipation in the continuous flow enables the exponential stabilization of these orbits through suitable feedback gains.

William Clark, Leonardo Colombo, Anthony Bloch2026-04-02⚡ eess