Explore advanced concepts in non-equilibrium statistical mechanics through this fourth lecture in a specialized physics series delivered at the VI Siembra-HoLAGrav Young Frontiers Meeting. Delve into the theoretical frameworks and mathematical tools used to analyze statistical systems that deviate from thermal equilibrium, examining how these systems evolve and respond to external perturbations. Learn about key principles governing non-equilibrium dynamics, including fluctuation theorems, response theory, and the role of entropy production in driven systems. Investigate applications to various physical phenomena such as active matter, quantum systems, and biological processes where equilibrium assumptions break down. Gain insights into cutting-edge research methodologies and computational approaches used to study complex non-equilibrium behavior in modern statistical physics.