相关论文: Hessian metric via transport information geometry
We introduce the concept of transport waves by showing that the linearized Boltzmann transport equation admits excitations in the form of waves that have well defined dispersion relations and decay times. Crucially, these waves do not…
We revisit a theory of heat transport in the light of a gauge theory of gravity and find the proper heat current with a corresponding gauge field, which yields the natural definitions of the heat magnetization and the Kubo-formula…
We investigate contraction of the Wasserstein distances on $\mathbb{R}^d$ under Gaussian smoothing. It is well known that the heat semigroup is exponentially contractive with respect to the Wasserstein distances on manifolds of positive…
We present the hydrodynamics of fluids in three spatial dimensions with helical symmetry, wherein only a linear combination of a rotation and translation is conserved in one of the three directions. The hydrodynamic degrees of freedom…
Understanding the space of probability measures on a metric space equipped with a Wasserstein distance is one of the fundamental questions in mathematical analysis. The Wasserstein metric has received a lot of attention in the machine…
This paper presents a new gradient flow dissipation geometry over non-negative and probability measures. This is motivated by a principled construction that combines the unbalanced optimal transport and interaction forces modeled by…
Bismuth is one of the rare materials in which second sound has been experimentally observed. Our exact calculations of thermal transport with the Boltzmann equation predict the occurrence of this Poiseuille phonon flow between $\approx$ 1.5…
The local-equilibrium approach to transport processes is related to the approach based on time-dependent correlation functions and their associated spectral functions characterizing the equilibrium fluctuations of particle, momentum and…
We derive equations for fluid dynamics from a non-extensive Boltzmann transport equation consistent with Tsallis' non-extensive entropy formula. We evaluate transport coefficients employing the relaxation time approximation and investigate…
This work studies the entropic regularization formulation of the 2-Wasserstein distance on an infinite-dimensional Hilbert space, in particular for the Gaussian setting. We first present the Minimum Mutual Information property, namely the…
Leveraging the Wasserstein distance -- a summation of sample-wise transport distances in data space -- is advantageous in many applications for measuring support differences between two underlying density functions. However, when supports…
Optimal transport provides a powerful mathematical framework with applications spanning numerous fields. A cornerstone within this domain is the $p$-Wasserstein distance, which serves to quantify the cost of transporting one probability…
We study hydrodynamic phonon heat transport in two-dimensional (2D) materials. Starting from the Peierls-Boltzmann equation within the Callaway model, we derive a 2D Guyer-Krumhansl-like equation describing non-local hydrodynamic phonon…
Thermal transport in classical fluids is analyzed in terms of a Higher-Order Generalized Hydrodynamics (or Mesoscopic Hydro-Thermodynamics), that is, depending on the evolution of the energy density and its fluxes of all orders. It is…
The Wasserstein metric is introduced as a probabilistic method to enable quantitative evaluations of LES combustion models. The Wasserstein metric can directly be evaluated from scatter data or statistical results using probabilistic…
Many scientific systems, such as cellular populations or economic cohorts, are naturally described by probability distributions that evolve over time. Predicting how such a system would have evolved under different forces or initial…
In the present thesis, we study the heat flow in mesoscopic one-dimensional transport systems. Using the analysis of full counting statistics, we calculate the cumulant generating function of the particle and heat flows and prove its…
The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…
We study the contraction in Wasserstein distance of the coordinate ascent variational inference algorithm. This is shown to hold under a transport-information inequality at the fixed points and a functional smoothness condition. The results…