Stochastic thermodynamics of imitation models

This thesis explores the application of Stochastic Thermodynamics (ST) as a robust framework for studying complex systems. For this purpose, we have focused on the context of sociophysics which lacks a clear thermodynamic foundation. Recent studies have already considered the application of ST to the majority-vote model and variations. However, these models are not microscopically reversible, which means that they generate irreversibility from its definition. In this work, we introduce a novel imitation model that is microscopically reversible and satisfies both Local and Global Detailed Balance conditions. This model challenges previous claims in the literature by demonstrating entropy production in systems satisfying global detailed balance. Moreover, in contrast to previous works, we focus on the mathematical application of ST to sociophysical systems, without the need to postulate an “energy” function. In this manner, we provide a more general framework for the study of complex systems, extending the applicability of ST beyond traditional physical systems. Our analysis includes both analytical and numerical methods to explore the model’s behavior, including equilibrium and stationary states, critical phenomena, and stochastic thermodynamics quantities. Our results demonstrate the potential of ST as a powerful tool for analyzing sociophysical models, offering a broader framework for studying complex systems.

Master Thesis defended by Luis Irisarri on 03/10/24.