⚡ Non-Equilibrium Statistical Mechanics

Derive the Boltzmann equation that describes the time evolution of distribution functions, and understand the entropy increase law through the H-theorem. Learn the treatment of collision terms and the relaxation time approximation, and numerically simulate the relaxation process of gas molecules using Python.

Derive the Master equation, which forms the basis of probabilistic descriptions, and understand the concepts of transition probability and detailed balance. Implement basic stochastic processes such as random walks and birth-death processes in Python and analyze their statistical properties.

Derive the Langevin equation describing the motion of particles in a heat bath, and understand the corresponding Fokker-Planck equation. Implement numerical solutions using the Euler-Maruyama method and verify the statistical properties of Brownian motion (mean square displacement, diffusion coefficient) in Python.

Learn linear response theory that describes the response of systems to external fields. Understand the Green-Kubo formula and Onsager reciprocity, and derive the fluctuation-dissipation theorem. Implement methods for calculating transport coefficients in Python.

Learn applications of non-equilibrium statistical mechanics to materials processes. Understand the theoretical framework of chemical reaction kinetics, solutions to diffusion equations, crystal growth dynamics, and phase separation kinetics, and implement practical materials process simulations in Python.