Probing Complexity, Universality and Dimensional Reduction in Nonequilibrium Statistical Physics

This thesis investigates universality and complexity in classical and quantum statistical physics, with a particular emphasis on nonequilibrium phenomena. While the emergence of universal behavior in equilibrium systems stands as one of the cornerstones of statistical physics, the extension of these ideas to nonequilibrium settings presents fundamental and still open challenges. The inherently diverse and system-specific nature of nonequilibrium dynamics calls for a broad spectrum of conceptual and analytical tools. Furthermore, nonequilibrium dynamics is nowadays accessible to experiments in both classical and quantum regimes. These modern experiments produce a large amount of experimental data, which calls for analysis of physics through data-driven methods, complexity theory and high-dimensional statistics. The possibility of probing and accessing correlated states of matter out of equilibrium in modern experiments raises several questions. Can we understand the output of experiments in terms of complexity theory and dimensional reduction? Is it possible to extend concepts of universality to data structures arising in simulations? Can we describe phase transitions (either classical or quantum) concepts of modern data science? How to control entanglement in quantum dynamics? Which nonequilibrium phenomena can we hope to observe in quantum simulators? The research work presented in this thesis is an attempt to answer to these questions. In this thesis, we argue that order parameters and diagnostics of criticality in nonequilibrium classical systems can be found by unsupervised learning and dimensional reduction, which allow to reduce the complexity of datasets by projections on lower-dimensional spaces, while still preserving essential universal features. We then move to the study of models of quantum dynamics relevant for quantum simulators. In particular, we show that the same concepts of dimensional reduction apply also to quantum systems, allowing for the extraction of information from outputs of quantum simulators. We then study a protocol to prepare complex, entangled states via unitary evolution and enhance entanglement via measurements in a fermionic model. Finally, we study the emergence of anomalous transport in one-dimensional chiral systems with non-Abelian symmetries.