Related papers: Gradient and Generic systems in the space of fluxe…
Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general non-quadratic dissipation potentials. This paper describes two natural…
Recent developments in Macroscopic Fluctuation Theory show that many interacting particle systems behave macroscopically as a combination of a gradient flow with Hamiltonian dynamics. This observation leads to the natural question how these…
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…
In this paper we discuss the connections between a Vlasov-Fokker-Planck equation and an underlying microscopic particle system, and we interpret those connections in the context of the GENERIC framework (\"Ottinger 2005). This…
We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where…
We consider the forward Kolmogorov equation corresponding to measure-valued processes stemming from a class of interacting particle systems in population dynamics, including variations of the Bolker-Pacala-Dieckmann-Law model. Under the…
In recent work [1] we uncovered intriguing connections between Otto's characterisation of diffusion as entropic gradient flow [16] on one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other.…
We study evolution equations on metric graphs with reservoirs, that is graphs where a one-dimensional interval is associated to each edge and, in addition, the vertices are able to store and exchange mass with these intervals. Focusing on…
At a continuous transition into a nonunique absorbing state, particle systems may exhibit nonuniversal critical behavior, in apparent violation of hyperscaling. We propose a generalized scaling theory for dynamic critical behavior at a…
The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods for diffusion models. We recall these properties and develop some new generic tools associated with the gradient…
We study a system of interacting particles that randomly react to form new particles. The reaction flux is the rescaled number of reactions that take place in a time interval. We prove a dynamic large-deviation principle for the reaction…
If gradient systems depend on a microstructure, we want to derive a macroscopic gradient structure describing the effective behavior of the microscopic effects. We introduce a notion of evolutionary Gamma-convergence that relates the…
We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these…
In this work, we investigate links between the formulation of the flow of marginals of reversible diffusion processes as gradient flows in the space of probability measures and path wise large deviation principles for sequences of such…
We propose a general coarse-graining method to derive a continuity equation that describes any dissipative system of repulsive particles interacting through short-ranged potentials. In our approach, the effect of particle-particle…
In systems of diffusing particles, we investigate large deviations of a time-averaged measure of clustering around one particle. We focus on biased ensembles of trajectories, which realise large-deviation events. The bias acts on a single…
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…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this…
We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…
It is well-known that many diffusion equations can be recast as Wasserstein gradient flows. Moreover, in recent years, by modifying the Wasserstein distance appropriately, this technique has been transferred to further evolution equations…