PHYS 5317 explores a range of topics that are central to understanding critical phenomena and non-equilibrium systems. Key areas of study include: Fluctuations and Critical Phenomena: Examination of how small changes at the microscopic level can lead to significant macroscopic effects near critical points. The Ising Model: Study of this mathematical model to understand phase transitions and magnetic properties of materials. The Master Equation: Analysis of time evolution in systems with probabilistic transitions between states. Transport in Solids: Investigation of how particles, energy, and other physical quantities move through solid materials. Chaos: Exploration of deterministic systems that exhibit unpredictable behavior due to sensitivity to initial conditions. Prerequisite: PHYS 5310.