Statistical Mechanics of Complex Systems (2024-25)
Welcome Message
Welcome to the course on Statistical Mechanics of Complex Systems! We are excited to have you embark on this journey into the fascinating world of statistical physics and complex systems. Throughout this course, you will develop a strong foundation in classical statistical mechanics while also exploring modern applications in stochastic dynamics, community modeling, and phase transitions. We encourage active participation, curiosity, and collaboration. Looking forward to a great academic year together!
Course Description and Goals
This course provides a comprehensive introduction to Statistical Mechanics, from fundamental classical principles to the study of complex systems. The goal is to equip students with analytical and computational tools to understand equilibrium and non-equilibrium statistical systems, stochastic processes, and phase transitions. Students will develop problem-solving skills applicable to physics, biology, and interdisciplinary fields.
Synthetic Program
First Part: Classical Statistical Mechanics (3 CFU)
Fundamental ensembles (micro-canonical, canonical, and grand-canonical), entropy, and thermodynamics.
Probability distributions, characteristic functions, and saddle-point approximations.
Maxwell velocity distribution, thermodynamic potentials, Legendre transforms, and phase space analysis.
Diffusion processes, stochastic processes, Markov processes, and the diffusion equation.
Second Part: Statistical Mechanics of Complex Systems (6 CFU)
Stochastic dynamics: Markov processes, master equations, and Langevin/Fokker-Planck equations.
Community dynamics: stochastic amplification, predator-prey models, and biodiversity theory.
Stochastic resonance, escape processes, first-passage times, and transition rates.
Spatial effects, voter models, and biodiversity calculations.
Lattice Gas and Ising Model: phase transitions, mean-field approximations, and critical behavior.
References
Lecture notes and textbooks by Sethna, Gardiner, Bressloff, and Baxter, along with key scientific publications, provide theoretical foundations and practical applications.
This course prepares students for advanced research in statistical mechanics and complex systems.
Welcome Message
Welcome to the course on Statistical Mechanics of Complex Systems! We are excited to have you embark on this journey into the fascinating world of statistical physics and complex systems. Throughout this course, you will develop a strong foundation in classical statistical mechanics while also exploring modern applications in stochastic dynamics, community modeling, and phase transitions. We encourage active participation, curiosity, and collaboration. Looking forward to a great academic year together!
Course Description and Goals
This course provides a comprehensive introduction to Statistical Mechanics, from fundamental classical principles to the study of complex systems. The goal is to equip students with analytical and computational tools to understand equilibrium and non-equilibrium statistical systems, stochastic processes, and phase transitions. Students will develop problem-solving skills applicable to physics, biology, and interdisciplinary fields.
Synthetic Program
First Part: Classical Statistical Mechanics (3 CFU)
Fundamental ensembles (micro-canonical, canonical, and grand-canonical), entropy, and thermodynamics.
Probability distributions, characteristic functions, and saddle-point approximations.
Maxwell velocity distribution, thermodynamic potentials, Legendre transforms, and phase space analysis.
Diffusion processes, stochastic processes, Markov processes, and the diffusion equation.
Second Part: Statistical Mechanics of Complex Systems (6 CFU)
Stochastic dynamics: Markov processes, master equations, and Langevin/Fokker-Planck equations.
Community dynamics: stochastic amplification, predator-prey models, and biodiversity theory.
Stochastic resonance, escape processes, first-passage times, and transition rates.
Spatial effects, voter models, and biodiversity calculations.
Lattice Gas and Ising Model: phase transitions, mean-field approximations, and critical behavior.
References
Lecture notes and textbooks by Sethna, Gardiner, Bressloff, and Baxter, along with key scientific publications, provide theoretical foundations and practical applications.
This course prepares students for advanced research in statistical mechanics and complex systems.
- Teacher: Amos Maritan