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Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the…

Structural causal models (SCMs), also known as (nonparametric) structural equation models (SEMs), are widely used for causal modeling purposes. In particular, acyclic SCMs, also known as recursive SEMs, form a well-studied subclass of SCMs…

Memory effects in the dynamics of open systems have been the subject of significant interest in the last decades. The methods involved in quantifying this effect, however, are often difficult to compute and may lack analytical insight. With…

In this chapter we summarize recent developments in the study of kinetically constrained models (KCMs) as models for glass formers. After recalling the definition of the KCMs which we cover we study the possible occurrence of ergodicity…

Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific…

We analyze a class of dynamics of open quantum systems which is governed by the dynamical map mutually commuting at different times. Such evolution may be effectively described via spectral analysis of the corresponding time dependent…

We propose a fully probabilistic formulation of the notion of mechanistic interaction (interaction in some fundamental mechanistic sense) between the effects of putative (possibly continuous) causal factors A and B on a binary outcome…

Discovering causal relations from observational time series without making the stationary assumption is a significant challenge. In practice, this challenge is common in many areas, such as retail sales, transportation systems, and medical…

We study the dynamics of quantum systems interacting with a stream of entangled qubits. Under fairly general conditions, we present a detailed framework describing the conditional dynamical maps for the system, called quantum trajectories,…

This Thesis explores how tools from Statistical Physics and Information Theory can help us describe and understand complex systems. In the first part, we study the interplay between internal interactions, environmental changes, and…

Strong zero modes (SZMs) are conserved operators localised at the edges of certain quantum spin chains, which give rise to long coherence times of edge spins. Here we define and analyse analogous operators in one-dimensional classical…

A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…

Robot navigation around humans can be a challenging problem since human movements are hard to predict. Stochastic model predictive control (MPC) can account for such uncertainties and approximately bound the probability of a collision to…

Topological phases support edge states that can be robust to material deformations and other perturbations. While well-studied in quantum systems, topological phases have also been observed in stochastic and biochemical systems, yet it…

A stochastic representation of the dynamics of open quantum systems, suitable for non-perturbative system-reservoir interaction, non-Markovian effects and arbitrarily driven systems is presented. It includes the case of driving on…

The concept of non-Markovianity in open quantum systems is traditionally associated with the existence of information backflows from the environment to the system. Meanwhile, the mechanisms through which such backflows emerge are still a…

It is known that the dynamical evolution of a system, from an initial tensor product state of system and environment, to any two later times, t1,t2 (t2>t1), are both completely positive (CP) but in the intermediate times between t1 and t2…

We introduce microscopic and macroscopic stochastic traffic models including traffic accidents. The microscopic model is based on a Follow-the-Leader approach whereas the macroscopic model is described by a scalar conservation law with…

The fragmentation of diatomic molecules under a stochastic force is investigated both classically and quantum mechanically, focussing on their dissociation probabilities. It is found that the quantum system is more robust than the classical…

We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…