In this thesis, we examine various systems through the lens of several numerical methods. We delve into questions concerning thermalization in closed unitary systems, lattice gauge theories, and... Show moreIn this thesis, we examine various systems through the lens of several numerical methods. We delve into questions concerning thermalization in closed unitary systems, lattice gauge theories, and the intriguing properties of deep neural network phase spaces. Leveraging modern advancements in both software and hardware, we scrutinize these systems in greater detail, accessing previously unreachable regimes. Show less
Systems with local constraints is a new finding in recent researches on complex systems. The heterogeneous spatial interactions and the temporal dependencies among those numerous units make it... Show moreSystems with local constraints is a new finding in recent researches on complex systems. The heterogeneous spatial interactions and the temporal dependencies among those numerous units make it difficult to describe by traditional statistical physics.These complex structures also make information storage and transmission in it is impossible to describe by the random variables with finite outcomes in the classical information theory. In this thesis, we use the statistical ensemble with local constraints to describe those complex systems with heterogeneous interactions and dependencies. This description also helps us find the new information-theoretical bounds in the systems with local constraints, even when the temporal dependencies among numerous units break the asymptotic equipartition property in the classical information theory.Furthermore, we find that the breaking of ensemble equivalence generally exists in systems with local constraints even without the presence of phase transition, and this ensemble nonequivalence in the systems with local constraints without phase transition can be the same strong as the one that only appears on the boundary of phase transitions caused by the long-range interactions. We also find that this breaking of ensemble equivalence will affect the limit of information storage and transmission in systems with local constraints.These results in this thesis extend our understanding of complex systems and information theory. Show less
In this thesis, "culture" refers to the collection of subjective human traits, such as preferences an opinions, that a given, geographically bounded population has at a given moment in time.... Show moreIn this thesis, "culture" refers to the collection of subjective human traits, such as preferences an opinions, that a given, geographically bounded population has at a given moment in time. Representative samples of individuals from such populations are studied, focusing on individual opinions expressed on various topics, present in multivariate empirical data that had been previously collected, mainly via social surveys. We propose and exploit new methods for analyzing such data, relying on mathematical notions specific to statistical mechanics and information theory, but also on agent-based models/simulations of opinion/cultural dynamics driven by social influence. These methods provide new insights about how human culture is organized. They provide indications that cultural structure has universal properties, independent of the geographical region and of the set of survey questions. Furthermore, these properties suggest that culture is shaped around a small number of "rationalities", while also having a certain hierarchical organization that is robust to social influence dynamics. Finally, we propose a method of filtering the noise in the data, which seems to allow for the identification of cultural modules that are not visible otherwise. However, we also show that visible modules may well be just artifacts of survey design. Show less
