Statistical Physics
LEARNING MODULE DESCRIPTION (SYLLABUS)
I. General information
1. Module title
Statistical Physics
2. Module code
04KOSWM – Fizyka statystyczna (dr P. Grzybowski) AMUPIE
3. Module type – compulsory or optional
compulsory
4. Programme title
5. Cycle of studies (1st or 2nd cycle of studies or full master’s programme)
1st
6. Year of studies (where relevant)
7. Terms in which taught (summer/winter term)
winter
8. Type of classes and the number of contact hours (e.g. lectures: 15 hours; practical classes: 30 hours)
lectures: 30 hours; classes: 15 hours
9. Number of ECTS credits
6
10. Name, surname, academic degree/title of the module lecturer/other teaching staff/ email
Przemysław, Grzybowski, PhD, grzyb@amu.edu.pl
11. Language of classes
English
II. Detailed information
1. Module aim (aims)
Basic course on Statistical Physics
2. Prerequisites in terms of knowledge, skills and social competences (where relevant)
Knowledge: Thermodynamics (X1A_W01), Classical Mechanics (X1A_W01), Quantum Mechanics (X1A_W01) multivariable calculus (X1A_W02)
Skills: Thermodynamics (X1A_U01), Classical Mechanics (X1A_U01), Quantum Mechanics (X1A_U01) multivariable calculus (X1A_U01)
3. Module learning outcomes in terms of knowledge, skills and social competences and their reference to programme learning outcomes
Learning outcomes symbol* 
Upon completion of the course, the student will: 
Reference to programme learning outcomes^{#} 
04KOSWM _01 
Knowledge: Student is able to explain the microscopic basis of thermodynamics: ergodic hypothesis, assumptions leading to microcanonical ensamble, statistical definition of entropy. 
X1A_W01 
04KOSWM _02 
Knowledge: Student is able to describe in detail the equilibrium statistical ensembles, in classical and quantum cases: microcanonical, canonical and grand canonical. 
X1A_W03 
04KOSWM _03 
Knowledge: Student knows basics of nonequlibrium thermodynamics: Boltzmann kinetic equation and Htheorem. 
X1A_W03 
04KOSWM _04 
Skills: Student uses equilibrium statistical ensembles to calculate basic physical quantities: energy, specific heat, entropy, in classical and quantum models. 
X1A_U01 
04KOSWM _05 
Skills: Student uses generalized equipartition theorem and Maxwell distribution of velocities and understands their limits. 
X1A_U01 
04KOSWM _06 
Skills: Student uses basic version of mean field theory for description of liquidgas and ferromagneticparamagnetic phase transitions in a simple models. 
X1A_U01 
* module code, e.g. KHT_01 (KHT – module code in USOS; stands for Polish “Kataliza Heterogeniczna” /Heterogeneous Catalysis/ )
^{#} programme learning outcomes (e.g. K_W01, K_U01, … ); first K stands for programme title symbol in Polish, W for “wiedza” (knowledge) in Polish, U – for “umiejętności” (skills) in Polish, K – for “kompetencje społeczne” (social competences) in Polish
01, 02…  learning outcome number
4. Learning content
Module title 

Learning content symbol* 
Learning content description 
Reference to module learning outcomes^{ #} 
TK_01 
Summary of thermodynamics: equilibrium, the laws of thermodynamics, thermodynamic definition of entropy, other thermodynamic potentials, thermodynamic relationships and identities. 
04KOSWM _01 
TK_02 
Elements of probability (probability distributions, cumulants, central limit theorem) 
04KOSWM _01 
TK_03 
Basic equilibrium statistical mechanics of classical systems: Gibbs statistical ensembles and the corresponding probabilities. The statistical definition of entropy. The partition function. Fluctuations of energy and number of particles – the equivalence of the ensembles. 
04KOSWM _01 ; 04KOSWM _02 ; 04KOSWM _04 
TK_04 
Selected applications of equilibrium statistical mechanics of classical systems: Maxwell velocity distribution, generalized equipartition theorem, the ideal gas, Gibbs paradox and proper Boltzmann counting. 
04KOSWM _05; 04KOSWM _04 
TK_05 
Elements of physics of phase transitions: the mean field theory for the gas van der Waals and derivation of the equation of state. Liquidgas transition as an example of a discontinuous transition, phase separation and Maxwell construction, metastable states. The mean field theory for the ferromagnetic Ising model. Ferromagneticparamagnetic transition as an example of continuous transitions, spontaneous symmetry breaking. The idea of universality and GinzburgLandau functional. 
04KOSWM _06 
TK_06 
Basics of equilibrium statistical mechanics of quantum systems: the concept of the pure state and mixed density operator, statistical ensembles. The quantum ideal gases: classical limit, degenerate fermion gas, BoseEinstein condensation. 
04KOSWM _02 
TK_07 
Elements of nonequilibrium statistical physics: Boltzmann kinetic equation, Htheorem and irreversibility, transport phenomena. 
04KOSWM _03 
* e.g. TK_01, TK_02, … (TK stands for “treści kształcenia” /learning content/ in Polish)
^{#} e.g. KHT_01 – module code as in Table in II.3
5. Reading list
F. Reif, „Statistical Mechanics”,
M. Kardar, „Statistical physics of particles”, Cambridge University Press (2007).
K. Huang, „Statistical mechanics”,
6. Information on the use of blendedlearning (if relevant)
7. Information on where to find course materials
III. Additional information
1. Reference of learning outcomes and learning content to teaching and learning methods and assessment methods
Module title 

Symbol of module learning outcome* 
Symbol of module learning content^{#} 
Methods of teaching and learning 
Assessment methods of LO achievement^{&} 
STAT_PH_01 
TK_01; TK_02; TK_03 
Lectures 
Exam 
STAT_PH_02 
TK_03; TK_06 
Lectures 
Exam 
STAT_PH_03 
TK_07 
Lectures 
Exam 
STAT_PH_04 
TK_03; TK_04 
Lectures, Classes 
50% Reports, 50% Exam 
STAT_PH_05 
TK_04 
Lectures, Classes 
50% Reports, 50% Exam 
STAT_PH_06 
TK_05 
Lectures, Classes 
50% Reports, 50% Exam 
* e.g. KHT_01 – module code as in Table in II.3 and II.4
^{#} e.g. TK_01 – learning content symbol as in II.4
^{&} Please include both formative (F) and summative (S) assessment
It is advisable to include assessment tasks (questions).
2. Student workload (ECTS credits)
Module title: 

Activity types 
Mean number of hours* spent on each activity type 
Contact hours with the teacher as specified in the programme 
45 
Independent study (4) writing a class report 
45 
Independent study (3) librarybased work 
45 
Total hours 
135 
Total ECTS credits for the module 
6 
* Class hours – 1 hour means 45 minutes
^{#}Independent study – examples of activity types: (1) preparation for classes, (2) data analysis, (3) librarybased work, (4)writing a class report, (5) exam preparation, etc.
3. Assessment criteria
4. Titles of classes
Syllabus: 

Week 1 
Summary of thermodynamics: equilibrium, the laws of thermodynamics, thermodynamic definition of entropy 
Week 2 
Summary of thermodynamics: thermodynamic potentials, thermodynamic relationships and identities 
Week 3 
Elements of probability (probability distributions, cumulants, central limit theorem) 
Week 4 
Basic equilibrium statistical mechanics of classical systems: Gibbs statistical ensembles and the corresponding probabilities. The statistical definition of entropy. 
Week 5 
Basic equilibrium statistical mechanics of classical systems: The partition function. Fluctuations of energy and number of particles – the equivalence of the ensembles. 
Week 6 
Selected applications of equilibrium statistical mechanics of classical systems: Maxwell velocity distribution, generalized equipartition theorem. 
Week 7 
Selected applications of equilibrium statistical mechanics of classical systems: The ideal gas, Gibbs paradox and proper Boltzmann counting. 
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. Liquidgas 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. Ferromagneticparamagnetic transition as an example of continuous transitions, spontaneous symmetry breaking. The idea of universality and GinzburgLandau 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 fermion gas. 
Week 12 
The quantum ideal gases: BoseEinstein condensation. 
Week 13 
Elements of nonequilibrium statistical physics: Boltzmann kinetic equation. 
Week 14 
Elements of nonequilibrium statistical physics: Htheorem and irreversibility. 
Week 15 
Elements of nonequilibrium statistical physics: transport phenomena. 