Syllabus
1) Stochastic dynamics: Introduction to random processes. Basics of stochastic description – stochastic trajectories (Langevin equation, simulations) vs. ensemble description (master equations).
Methods of solution. 2) Stochastic thermodynamics: Consistent thermodynamic descriptions (fluctuation-dissipation theorem, detailed balance condition). Definitions of heat, work, and entropy for individual trajectories of stochastic processes.
Fluctuation theorems, thermodynamic uncertainty relations, and their consequences. 3) Active matter: Basics of wet active matter and its hydrodynamic description. Dry active matter – active Brownian particles, active Ornstein–Uhlenbeck process, Vicsek model.
Basic solutions and results.
Annotation
Modern applications of statistical physics: basic theoretical concepts and key results of stochastic dynamics and thermodynamics and active matter. Langevin and master equations and methods of their solution. Fluctuation- dissipation theorem. Detailed balance. Fluctuation theorems. Thermodynamic uncertainty relations. Active
Brownian particles. Vicsek model.