math-ph papers | Gist.Science

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

On the commutation of variation and differentiation in nonholonomic Systems: A Chetaev-based approach

This paper resolves the tension between d'Alembert-Lagrange and integral variational approaches in nonholonomic mechanics by demonstrating that the commutation of variation and differentiation is generally incompatible with Chetaev's principle unless specific geometric conditions are met, while revealing that dynamic consistency can emerge as a collective phenomenon where interactions between multiple non-integrable constraints cancel out deviations from holonomy.

Federico Talamucci2026-02-05

🔢 mathematics

On the local nature of the de Almeida-Thouless line for mixed $p$ -spin glasses

This paper refutes the claim that a generalized de Almeida-Thouless criterion proposed by Jagannath and Tobasco universally characterizes the replica symmetric regime in mixed $p$ -spin glasses by constructing explicit counterexamples using the Hopf-Lax representation of the Parisi formula, while noting that the validity of the classical condition for the Sherrington-Kirkpatrick model remains an open question.

Jean-Christophe Mourrat, Adrien Schertzer2026-02-05

🔢 mathematics

Interpretation of stochastic primitive equations with relaxed hydrostatic assumption as a higher order approximation of 3D stochastic Navier-Stokes

This paper establishes the convergence of solutions from a stochastic 3D Navier-Stokes system to a generalized stochastic primitive equation model that incorporates relaxed hydrostatic assumptions via martingale terms, demonstrating that this modified framework serves as a well-posed, higher-order approximation of the original equations under specific asymptotic scalings and boundary conditions.

Arnaud Debussche, Étienne Mémin, Antoine Moneyron2026-02-05

🔢 mathematics

Brownian paths as loop-decorated SLEs

This paper resolves a conjecture by Lawler and Werner by proving that chronologically adding loops from a Brownian loop soup to an independent radial SLE $_2$ path yields a planar Brownian motion, thereby establishing a robust coupling between these processes as the scaling limit of loop-erased random walks and random walks.

Nathanaël Berestycki, Isao Sauzedde2026-02-05

🔢 mathematics

Intrinsic Ultracontractivity for a class of Schroedinger Semigroups in $L^{2}(\mathbb{R}^{n})$ by Logarithmic Sobolev inequalities

This paper establishes a growth condition on the potential $q$ of a Schrödinger operator that implies Rosen inequalities for its ground state, which are then utilized to derive Logarithmic Sobolev inequalities and prove the intrinsic ultracontractivity of the associated Schrödinger semigroup.

Christoph Schwerdt, Alexander Mill, Dirk Hundertmark2026-02-05

🔢 mathematics

Intrinsic Ultracontractivity for a class of Schroedinger Semigroups in $\mathrm{L}^{2}\left( \mathbb{R}^{n} \right)$ using Log-Sobolev-inequalities and duality arguments

This paper establishes the intrinsic ultracontractivity of weighted Schrödinger semigroups for a specific class of positive potentials by utilizing logarithmic Sobolev inequalities and duality arguments to prove continuous mapping between weighted $L^1$ and $L^2$ spaces.

Christoph Schwerdt, Ilham Ouelddris2026-02-05

🔢 mathematics

Pairs of differential forms: a framework for precontact geometry

This paper establishes a geometric framework for precontact manifolds by analyzing general pairs of 1-forms and 2-forms under mild regularity conditions, characterizing their properties, defining associated vector fields and Hamiltonian dynamics, and illustrating the theory with various examples.

Xavier Gràcia, Àngel Martínez-Muñoz, Xavier Rivas2026-02-05

🔢 mathematics

A radiation and propagation problem for a Helmholtz equation with a compactly supported nonlinearity

This paper extends a theoretical and numerical framework for analyzing scattering on infinite plates to general two- and three-dimensional objects with compactly supported nonlinearities by transforming the full-space nonlinear Helmholtz equation into an equivalent bounded boundary-value problem using a nonlocal Dirichlet-to-Neumann operator, thereby enabling unique solutions and efficient finite element approximations.

Lutz Angermann2026-02-04

🔢 mathematics

Two invariant subalgebras of rational Cherednik algebras

This paper investigates the ring-theoretic and homological properties of two invariant subalgebras of rational Cherednik algebras by realizing them as rings of invariants under reductive subgroups of $\rm SL_2$ , thereby characterizing their centers, establishing their Cohen-Macaulay and Auslander-Gorenstein nature, and analyzing their quantum Hamiltonian reductions at parameters $t=0$ and $t=1$ .

Gwyn Bellamy, Misha Feigin, Niall Hird2026-02-04

🧬 biology

Neural Thermodynamics: Entropic Forces in Deep and Universal Representation Learning

This paper proposes a rigorous entropic-force theory demonstrating that stochasticity and discrete-time updates in neural network training generate emergent forces that break continuous symmetries to explain universal representation alignment, the Platonic Representation Hypothesis, and the reconciliation of sharpness- and flatness-seeking optimization behaviors.

Liu Ziyin, Yizhou Xu, Isaac Chuang2026-02-04

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math-ph

On the commutation of variation and differentiation in nonholonomic Systems: A Chetaev-based approach

On the local nature of the de Almeida-Thouless line for mixed ppp-spin glasses

Interpretation of stochastic primitive equations with relaxed hydrostatic assumption as a higher order approximation of 3D stochastic Navier-Stokes

Brownian paths as loop-decorated SLEs

Intrinsic Ultracontractivity for a class of Schroedinger Semigroups in L2(Rn)L^{2}(\mathbb{R}^{n})L2(Rn) by Logarithmic Sobolev inequalities

Intrinsic Ultracontractivity for a class of Schroedinger Semigroups in L2(Rn)\mathrm{L}^{2}\left( \mathbb{R}^{n} \right)L2(Rn) using Log-Sobolev-inequalities and duality arguments

Pairs of differential forms: a framework for precontact geometry

A radiation and propagation problem for a Helmholtz equation with a compactly supported nonlinearity

Two invariant subalgebras of rational Cherednik algebras

Neural Thermodynamics: Entropic Forces in Deep and Universal Representation Learning

On the local nature of the de Almeida-Thouless line for mixed $p$ -spin glasses

Intrinsic Ultracontractivity for a class of Schroedinger Semigroups in $L^{2}(\mathbb{R}^{n})$ by Logarithmic Sobolev inequalities

Intrinsic Ultracontractivity for a class of Schroedinger Semigroups in $\mathrm{L}^{2}\left( \mathbb{R}^{n} \right)$ using Log-Sobolev-inequalities and duality arguments