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 derive the Hessian geometric structure of nonequilibrium chemical reaction networks on
the flux and force spaces induced by the Legendre duality of convex dissipation functions …

It is known that the distribution of nonreversible Markov processes breaking the detailed
balance condition converges faster to the stationary distribution compared to reversible …

We introduce a new information-geometric structure associated with the dynamics on
discrete objects such as graphs and hypergraphs. The presented setup consists of two …

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 …

We consider two approaches to study non-reversible Markov processes, namely the
hypocoercivity theory and general equations for non-equilibrium reversible–irreversible …

We study the convergence of a sequence of evolution equations for measures supported on
the nodes of a graph. The evolution equations themselves can be interpreted as the forward …

This thesis consists of two parts, both focusing on mean-field limits for interacting particle
systems, which describe the macroscopic behaviour of the system as the number of particles …

We describe reactive fluid flows in terms of the formalism General Equation for Non‐
Equilibrium Reversible‐Irreversible Coupling also known as GENERIC. We present the …

Using the theory of large deviations, macroscopic fluctuation theory provides a framework to
understand the behavior of nonequilibrium dynamics and steady states in diffusive systems …