This course provides a systematic introduction to modern nonequilibrium statistical physics. While equilibrium statistical mechanics is well established through ensemble theory and thermodynamics, the theoretical framework for nonequilibrium phenomena remains an active and evolving field of research. We will develop the fundamental principles governing irreversible processes, fluctuations, transport phenomena, and stochastic dynamics. The course integrates classical foundations (linear response theory, transport coefficients) with modern developments in stochastic thermodynamics and fluctuation theorems. Emphasis will be placed on conceptual clarity, mathematical formulation, and problem-solving skills.

COURSE OBJECTIVES
By the end of the course, students will be able to:

• Understand the origin of macroscopic irreversibility from microscopic dynamics.
• Derive linear response formulae and compute transport coefficients.
• Apply fluctuation—dissipation relations and Onsager reciprocity.
• Formulate master equations and Fokker—Planck equations.
• Solve stochastic differential equations (Langevin dynamics).
• Understand entropy production and nonequilibrium steady states.
• Apply fluctuations theorems (Jarzynski equality, Crooks theorem).
• Analyze stochastic thermodynamics at the trajectory level.

• Graduate-level equilibrium statistical mechanics
• Classical mechanics
• Basic knowledge of probability theory
However, it is ok to enroll in this course without this prerequisite knowledge.

• R. Kubo, Statistical Physics II: Nonequilibrium Statistical Mechanics, 2nd Ed., Springer.
• G. F. Mazenko, Nonequilibrium Statistical Mechanics, Wiley-VCH (2006).
• H. Risken, The Fokker-Planck Equation, 2nd Ed., Springer.
• W. Sung, Lecture note on nonequilibrium statistical physics (unpublished).

Part I: Foundations and Linear Response Theory
• Macroscopic irreversibility and entropy production
• Linear force-flux relations
• Onsager reciprocal relations and time-reversal symmetry
• Phenomenological transport coefficients
• Linear response theory
• Kubo formula
• Fluctuation–dissipation theorem
• Onsager reciprocal relations
• Green–Kubo relations
• Transport coefficients (diffusion, conductivity, viscosity)

Part II: Theory of Stochastic Processes
• Markov processes
• Master equation
• Detailed balance and steady states
• Continuous limit and Fokker–Planck equation
• Langevin equation
• Itô and Stratonovich calculus
• Probability currents and nonequilibrium steady states

Part III: Stochastic Thermodynamics
• Thermodynamics at the trajectory level
• Work and heat in stochastic systems
• Entropy production
• Jarzynski equality
• Crooks fluctuation theorem
• Breaking detailed balance
• Thermodynamic uncertainty relation
• Nonequilibrium steady states

The lecture will be given in the lecture hall using the chalkboard. Depending on the situation, Zoom-based online lectures will be used as an alternative.

See the syllabus material in the annoucement board.