In these notes we discuss general approaches for rigorously deriving limits of generalized
gradient flows. Our point of view is that a generalized gradient system is defined in terms of …

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 …

Abstract Onsager's 1931 “reciprocity relations” result connects microscopic time reversibility
with a symmetry property of corresponding macroscopic evolution equations. Among the …

We study a class of nonlocal partial differential equations presenting a tensor-mobility, in
space, obtained asymptotically from nonlocal dynamics on localising infinite graphs. Our …

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

We introduce two new concepts of convergence of gradient systems (Q, E _ ε, R _ ε)(Q, E ε,
R ε) to a limiting gradient system (Q, E _0, R _0)(Q, E 0, R 0). These new concepts are called …

The present notes provide an extended version of a small lecture course given at the
Humboldt Universit\" at zu Berlin in the Winter Term 2022/23 (of 36 hours). The material …

Most biochemical reactions in living cells are open systems interacting with environment
through chemostats to exchange both energy and materials. At a mesoscopic scale, the …

We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast
reactions. It is known that the fast-reaction-rate limit can be described by an ODE with …