Integrated Information and Complexity Measures for Disordered Systems

• Ano de defesa: 2023
• Autor(a) principal: Citton, Otávio Cístolo
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Complex Systems; Complexity Index; Disordered Systems; Índices de Compelxidade; Informação Integrada; Integrated Information; Mecânica Estatística; Sistemas Complexos; Sistemas Desordenados; Statistical Mechanics
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/43/43134/tde-15062023-052053/

Motivated by the possible applications that a better understanding of consciousness might bring, we follow Tononi\'s idea and calculate analytically a complexity index for a disordered system. Utilizing the information geometry formulation of integrated information theory, and by restricting our analysis to bipartitions of the system, we calculate the geometric integrated information index for the model we call Little-Sherrington-Kirkpatrick, a synchronous dynamics version of the SK spin-glass model with quenched Gaussian interactions. The effects of partitioning are taken into account by introducing site dilution. We show that this complexity index can be used to rank the three phases of the system in terms of its complexity, and make an analysis on how it changes when we vary the partitioning of the system. Finally, by approximating the dynamics near-equilibrium, we briefly analyze the behavior of the geometric integrated information index out of equilibrium.