Related papers: From a large-deviations principle to the Wasserste…
The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
We consider a class of time-homogeneous diffusion processes on $\mathbb{R}^{n}$ with common invariant measure but varying volatility matrices. In Euclidean space, we show via stochastic control of the diffusion coefficient that the…
Diffusion-based models on continuous spaces have seen substantial recent progress through the mathematical framework of gradient flows, leveraging the Wasserstein-2 (${W}_2$) metric via the Jordan-Kinderlehrer-Otto (JKO) scheme. Despite the…
In finite dimension, the long-time and metastable behavior of a gradient flow perturbated by a small Brownian noise is well understood. A similar situation arises when a Wasserstein gradient flow over a space of probability measure is…
We study a system of drift-diffusion PDEs for a potentially infinite number of incompressible phases, subject to a joint pointwise volume constraint. Our analysis is based on the interpretation as a collection of coupled Wasserstein…
In this paper, we start from a very natural system of cross-diffusion equations, which can be seen as a gradient flow for the Wasserstein distance of a certain functional. Unfortunately, the cross-diffusion system is not well-posed, as a…
Let K be an irreducible and reversible Markov kernel on a finite set X. We construct a metric W on the set of probability measures on X and show that with respect to this metric, the law of the continuous time Markov chain evolves as the…
We establish the gradient flow representation of diffusion with mobility $b$ with respect to the modified Wasserstein quasi-metric $W_h$, where $h(r)=rb(r)$. The appropriate selection of the free energy functional depends on the specific…
A nonlinear parabolic equation of sixth order is analyzed. The equation arises as a reduction of a model from quantum statistical mechanics, and also as the gradient flow of a second-order information functional with respect to the…
We revisit the variational characterization of diffusion as entropic gradient flux and provide for it a probabilistic interpretation based on stochastic calculus. It was shown by Jordan, Kinderlehrer, and Otto that, for diffusions of…
Motivated by a probabilistic approach to Kahler-Einstein metrics we consider a general non-equilibrium statistical mechanics model in Euclidean space consisting of the stochastic gradient flow of a given (possibly singular) quasi-convex…
The propagation of gradient flow structures from microscopic to macroscopic models is a topic of high current interest. In this paper we discuss this propagation in a model for the diffusion of particles interacting via hard-core exclusion…
In this work, we investigate a variational formulation for a time-fractional Fokker-Planck equation which arises in the study of complex physical systems involving anomalously slow diffusion. The model involves a fractional-order Caputo…
We revisit the variational characterization of conservative diffusion as entropic gradient flow and provide for it a probabilistic interpretation based on stochastic calculus. It was shown by Jordan, Kinderlehrer, and Otto that, for…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
Purely dissipative evolution equations are often cast as gradient flow structures, $\dot{\mathbf{z}}=K(\mathbf{z})DS(\mathbf{z})$, where the variable $\mathbf{z}$ of interest evolves towards the maximum of a functional $S$ according to a…
We compute the entropy production engendered in the environment from a single Brownian particle which moves in a mean flow, and show that it corresponds in expectation to classical near-equilibrium entropy production in the surrounding…
We prove the equivalence between the notion of Wasserstein gradient flow for a one-dimensional nonlocal transport PDE with attractive/repulsive Newtonian potential on one side, and the notion of entropy solution of a Burgers-type scalar…
Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the…