## General information

Course type | AMUPIE |

Module title | Statistical Physics |

Language | English |

Module lecturer | dr Przemysław Grzybowski |

Lecturer's email | grzyb@amu.edu.pl |

Lecturer position | Adjunct |

Faculty | Faculty of Physics |

Semester | 2022/2023 (winter) |

Duration | 60 |

ECTS | 5 |

USOS code | 04-W-STPH-45 |

## Timetable

30 hours of Lectures (15 Lectures) and 30 hours of Classes (15 Classes)

## Module aim (aims)

It is basic course on Statistical Physics. It aims are:

1) Introduction of basic concepts and methods of Statistical Physics

2) Introduction of basic equilibrium ensembles and their properties.

3) Basic applications and illustration of problems with interacting systems.

4) Introduction of basic quantum equilibrium ensembles

5) Introduction to basic non-equilibrium approaches

## Pre-requisites in terms of knowledge, skills and social competences (where relevant)

Knowledge: Thermodynamics, Classical Mechanics, Basic Quantum Mechanics, Multivariable Calculus.

Skills: Calculus: Thermodynamics, Classical Mechanics, Basic Quantum Mechanics,

## Syllabus

Week 1: Summary of thermodynamics: equilibrium, the laws of thermodynamics, thermodynamic definition of entropy, thermodynamic potentials, thermodynamic relationships and identities.

Week 2: Configurations, Deterministic evolution and Liouville Theorem, Ergodic hypothesis. Elements of theory of probability (probability distributions, cumulants, central limit theorem)

Week 3: Basic equilibrium statistical mechanics of classical systems: Gibbs statistical ensembles and the corresponding probabilities. Introduction of statistical definition of entropy.

Week 4: Statistical definition of entropy - properties, interpretation. Laser and anti-Boltzmann states.

Week 5: Basic equilibrium statistical mechanics of classical systems: The partition functions and related thermodynamic potentials. Fluctuations of energy and number of particles – the equivalence of the ensembles.

Week 6: Selected applications of equilibrium statistical mechanics of classical systems: The ideal gas, Gibbs paradox and proper Boltzmann counting.

Week 7: Selected applications of equilibrium statistical mechanics of classical systems: Maxwell velocity distribution, generalized equipartition theorem.

Week 8: Elements of physics of phase transitions: the mean field theory for the gas van der Waals and derivation of the equation of state. Liquid-gas transition as an example of a discontinuous transition, phase separation and Maxwell construction, metastable states.

Week 9: Elements of physics of phase transitions: The mean field theory for the ferromagnetic Ising model. Ferromagnetic-paramagnetic transition as an example of continuous transitions, spontaneous symmetry breaking. The idea of universality and Ginzburg-Landau functional.

Week 10: Basics of equilibrium statistical mechanics of quantum systems: the concept of the pure state and mixed density operator, statistical ensembles.

Week 11: The quantum ideal gases: classical limit, degenerate Fermi gas.

Week 12: The quantum ideal gases: Bose-Einstein condensation, black body radiation

Week 13: Elements of non-equilibrium statistical physics: Boltzmann kinetic equation and transport phenomena.

Week 14: Information and Irreversibility from the perspective of Statistical Physics

Week 15: Elements of non-equilibrium statistical physics: Jarzynski equality and Fluctuation theorems

## Reading list

- F. Reif, „Statistical Mechanics”,
- M. Kardar, „Statistical physics of particles”, Cambridge University Press (2007),
- K. Huang, „Statistical mechanics”,