相关论文: On Harnack inequalities and optimal transportation

The Onsager-de Groot-Callen transport theory, implemented as a network model, is used to simulate the transient Harman method, which is widely used experimentally to determine all thermoelectric transport coefficients in a single…

This paper presents analogous results for stochastic fast-diffusion equations. Since the fast-diffusion equation possesses weaker dissipativity than the porous medium one does, some technical difficulties appear in the study. As a…

We consider second-order linear parabolic operators in non-divergence form that are intrinsically defined on Riemannian manifolds. In the elliptic case, Cabr\'e proved a global Krylov-Safonov Harnack inequality under the assumption that the…

Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…

Heat transport in open quantum systems is particularly susceptible to the modeling of system-reservoir interactions. It thus requires to consistently treat the coupling between a quantum system and its environment. While perturbative…

Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…

In this work, we investigate the heat flow of two interacting quantum systems on the perspective of noncommutativity phase-space effects and show that by controlling the new constants introduced in the quantum theory, due to a deformed…

We consider the evolution of hypersurfaces on the unit sphere $\mathbb{S}^{n+1}$ by their mean curvature. We prove a differential Harnack inequality for any weakly convex solution to the mean curvature flow. As an application, by applying…

In this paper, we first derive a Sobolev inequality along the harmonic-Ricci flow. We then prove a linear parabolic estimate based on the Sobolev inequality and Moser's iteration. As an application, we will obtain an upper bound estimate…

Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this…

By using coupling and Girsanov transformations, the dimension-free Harnack inequality and the strong Feller property are proved for transition semigroups of solutions to a class of stochastic generalized porous media equations. As…

We study heat transport in normal/superconducting graphene junctions. We find that while the thermal conductance displays the usual exponential dependence on temperature, reflecting the s-wave symmetry of the superconductor, it exhibits an…

We propose a geometric theory of non-equilibrium thermodynamics, namely geometric thermodynamics, using our recent developments of differential-geometric aspects of entropy production rate in non-equilibrium thermodynamics. By revisiting…

We build upon a recently introduced class of quasi-graph random features (q-GRFs), which have demonstrated the ability to yield lower variance estimators of the 2-regularized Laplacian kernel (Choromanski 2023). Our research investigates…

We obtain explicit mean value formulas for the solutions of the diffusion equations associated with the Ornstein-Uhlenbeck and Hermite operators. From these, we derive various useful properties, such as maximum principles, uniqueness…

We study the horizontal Laplacian $\Delta^H$ associated to the Hopf fibration $S^3\to S^2$ with arbitrary Chern number $k$. We use representation theory to calculate the spectrum, describe the heat kernel and obtain the complete heat trace…

Understanding nanoscale hotspot thermal transport is crucial in electronic devices. Contrary to common perception, recent experiments show that closely spaced nanoscale multiple hotspots can enhance heat dissipation. Here, the thermal…

In [10], R. Hamilton established a differential Harnack inequality for solutions to the Ricci flow with nonnegative curvature operator. We show that this inequality holds under the weaker condition that M x R^2 has nonnegative isotropic…

In one and two dimensions, transport coefficients may diverge in the thermodynamic limit due to long--time correlation of the corresponding currents. The effective asymptotic behaviour is addressed with reference to the problem of heat…

We investigate the two-dimensional transport of heat through viscous flow between two parallel rough interfaces with a given fractal geometry. The flow and heat transport equations are solved through direct numerical simulations, and for…