Um estudo sobre termodinâmica e informação em modelos holográficos

Abstract

This dissertation addresses aspects of information theory and thermodynamics in the context of gauge/gravity duality, focusing on two specific holographic models: 1RCBH and 2RCBH. The study analyzes fundamental concepts of information theory, such as entanglement entropy and discusses gauge/gravity duality as a tool for analyzing thermodynamic and information properties of these models. Initially, we review in detail the thermodynamics of the 1RCBH model, which is a toy-model for a strongly-coupled quantum field theory at finite temperature and density and has a critical point in its phase diagram, while the 2RCBH model describes a different strongly-coupled quantum field theory, also defined at finite temperature and density, but without a critical point in its phase diagram. The main focus of the research is to calculate thermodynamic and information observables using holographic gauge/gravity duality in these models. We also review the entanglement entropy of the 1RCBH model, and, as an original contribution, we propose a new and more efficient method to evaluate it than previously considered in the literature. Due to some numerical issues still to be understood and solved, a detailed analysis of the entanglement entropy in the 1RCBH and 2RCBH models will be postponed to an upcoming work intended for publication.