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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.
Last update: Búryová Marcela (27.05.2021)
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Introduction to rapidly evolving parts of nonequilibrium statistical physics with a focus on their applications in biophysics. Stochastic thermodynamics studies energy transport and transformation processes on micro-scale of cells and even quantum systems. Active matter theory describes systems composed of non-equilibrium ``molecules’’ such as bacteria, insects, or birds.
The course is suitable for students of experimental biophysics, chemical physics, and theoretical biophysics, who wish to learn current methods of inferring thermodynamic quantities, such as free energy profiles or entropy production, from measured or simulated data. It is also intended for students of theoretical physics with a focus on statistical physics and thermodynamics, whose modern developments are covered in the course. Last update: Holubec Viktor, doc. RNDr., Ph.D. (16.06.2025)
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Přednáška nebo konzultace podle počtu studentů. Některá probíraná témata je možno volit dle aktuálních potřeb studentů.
Last update: Holubec Viktor, doc. RNDr., Ph.D. (16.06.2025)
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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 (Jarzynski equality and Crooks fluctuation theorem) as generalizations of the second law of thermodynamics and their applications to the calculation of equilibrium free energies via nonequilibrium experiments and molecular dynamics simulations. Thermodynamic uncertainty relations and their application to estimating entropy production in nonequilibrium processes.
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. Last update: Holubec Viktor, doc. RNDr., Ph.D. (19.06.2025)
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