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

We consider dynamical transport metrics for probability measures on discretizations of a
bounded convex domain in \mathbbR^d. These metrics are natural discrete counterparts to …

The dynamics of probability density functions has been extensively studied in science and
engineering to understand physical phenomena and facilitate algorithmic design. Of …

We consider dynamics driven by interaction energies on graphs. We introduce graph
analogues of the continuum nonlocal-interaction equation and interpret them as gradient …

We study quantum Dirichlet forms and the associated symmetric quantum Markov
semigroups on noncommutative $ L^ 2$ spaces. It is known from the work of Cipriani and …

In this paper we investigate the numerical approximation of an analogue of the Wasserstein
distance for optimal transport on graphs that is defined via a discrete modification of the …

We consider finite-volume approximations of Fokker--Planck equations on bounded convex
domains in R^d and study the corresponding gradient flow structures. We reprove the …

In this article we study the noncommutative transport distance introduced by Carlen and
Maas and its entropic regularization defined by Becker and Li. We prove a duality formula …

We consider a point cloud X_n:={x _1, ..., x _n\} X n:= x 1,…, xn uniformly distributed on the
flat torus T^ d:= R^ d/Z^ d T d:= R d/Z d, and construct a geometric graph on the cloud by …

The seminal result of Benamou and Brenier provides a characterization of the Wasserstein
distance as the path of the minimal action in the space of probability measures, where paths …