Abstract We study the McKean–Vlasov equation ∂ _t ϱ= β^-1 Δ ϱ+ κ\, ∇ ⋅\,(ϱ ∇ (W ⋆
ϱ)),∂ t ϱ= β-1 Δ ϱ+ κ∇·(ϱ∇(W⋆ ϱ)), with periodic boundary conditions on the torus. We …

We have created a functional framework for a class of non-metric gradient systems. The
state space is a space of nonnegative measures, and the class of systems includes the …

We review a class of gradient systems with dissipation potentials of hyperbolic-cosine type.
We show how such dissipation potentials emerge in large deviations of jump processes …

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 the nonlinear Fokker-Planck equation on graphs, which is the gradient flow in the
space of probability measures supported on the nodes with respect to the discrete …

In this paper, we explore the convergence of the semi-discrete Scharfetter–Gummel scheme
for the aggregation-diffusion equation using a variational approach. Our investigation …

Consider the Monge-Kantorovich problem of transporting densities $\rho_0 $ to $\rho_1 $
on $\mathbb {R}^ d $ with a strictly convex cost function. A popular relaxation of the problem …

We consider various modeling levels for spatially homogeneous chemical reaction systems,
namely the chemical master equation, the chemical Langevin dynamics, and the reaction …

In this paper we propose a finite-volume scheme for aggregation–diffusion equations based
on a Scharfetter–Gummel approximation of the quadratic, nonlocal flux term. This scheme is …

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 …