Motivated by the occurrence in rate functions of time-dependent large-deviation principles,
we study a class of non-negative functions ℒ that induce a flow, given by ℒ (ρ t, ρ ̇ t)= 0 …

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 …

Chemical reaction networks offer a natural nonlinear generalization of linear Markov jump
processes on a finite state-space. In this paper, we analyze the dynamical large deviations …

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

When thermodynamics is understood as the science (or art) of constructing effective models
of natural phenomena by choosing a minimal level of description capable of capturing the …

We show that all Lindblad operators (ie, generators of quantum Markov semigroups) on a
finite-dimensional Hilbert space satisfying the detailed balance condition with respect to the …

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 …

In molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining
is an important technique to reduce the dimensionality of the problem. We will study and …

The Dean--Kawasaki model consists of a nonlinear stochastic partial differential equation
featuring a conservative, multiplicative, stochastic term with non-Lipschitz coefficient, driven …