The Wasserstein distance is an attractive tool for data analysis but statistical inference is
hindered by the lack of distributional limits. To overcome this obstacle, for probability …

We study a class of ergodic quantum Markov semigroups on finite-dimensional unital C⁎-
algebras. These semigroups have a unique stationary state σ, and we are concerned with …

We introduce a general notion of transport cost that encompasses many costs used in the
literature (including the classical one and weak transport costs introduced by Talagrand and …

We consider finite-dimensional, time-continuous Markov chains satisfying the detailed
balance condition as gradient systems with the relative entropy E as driving functional. The …

We propose a housekeeping/excess decomposition of entropy production for general
nonlinear dynamics in a discrete space, including chemical reaction networks and discrete …

Let CC denote the Clifford algebra over R^ n R n, which is the von Neumann algebra
generated by n self-adjoint operators Q j, j= 1,…, n satisfying the canonical anticommutation …

We study dynamical optimal transport metrics between density matrices associated to
symmetric Dirichlet forms on finite-dimensional C^* C∗-algebras. Our setting covers …

Metric measure spaces with synthetic Ricci bounds have attracted great interest in recent
years, accompanied by spectacular breakthroughs and deep new insights. In this survey, I …

Abstract While Graph Neural Networks (GNNs) have been successfully leveraged for
learning on graph-structured data across domains, several potential pitfalls have been …

We consider systems of reaction–diffusion equations as gradient systems with respect to an
entropy functional and a dissipation metric given in terms of a so-called Onsager operator …