COURSE GOALS: Understandig the relationship between thermodynamics and statistical physics. Acquiring the basic concepts of the statistical description of a system in the thermodynamic limit: entropy, thermodynamic potentials, ensemble, single-particle distributions, fluctuations.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
Upon completing the degree, students will be able to:
1. KNOWLEDGE AND UNDERSTANDING
1.1 formulate, discuss and explain the basic laws of physics including mechanics, electromagnetism and thermodynamics
1.3 demonstrate a thorough knowledge of the most important physics theories (logical and mathematical structure, experimental support, described physical phenomena)
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.1 identify the essentials of a process/situation and set up a working model of the same or recognize and use the existing models
2.2 evaluate clearly the orders of magnitude in situations which are physically different, but show analogies, thus allowing the use of known solutions in new problems;
2.4 adapt available models to new experimental data
3. MAKING JUDGEMENTS
3.1 work with a high degree of autonomy, even accepting responsibilities in project planning and in the managing of structures
3.2 develop a personal sense of responsibility, given the free choice of elective/optional courses
3.3 comprehend the ethical characteristics of research and of the professional activity in physics
4. COMMUNICATION SKILLS
4.1 work in an interdisciplinary team
5. LEARNING SKILLS
5.1 search for and use physical and other technical literature, as well as any other sources of information relevant to research work and technical project development (good knowledge of technical English is required)
5.3 carry out research by undertaking a PhD
5.4 participate in projects which require advanced skills in modeling, analysis, numerical calculations and use of technologies
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
By the end of the course, the student should be able to:
1. understand abstract thermodynamics at the elementary level of the theory of functions of several variables;
2. explain the difference between thermodynamics and theoretical mechanics, i.e. thermalization as a real physical process;
3. explain the role of thermalization and the Liouville theorem in the foundations of statistical physics;
4. explain the physical construction of thermodynamic potentials through the energy of interaction of a system and the outside world;
5. understand the statistical interpretation of thermodynamic potentials, particularly the entropy and Massieu functions;
6. explain the role of the chemical potential and its qualitative behavior in the classical and quantum limits;
7. describe five ideal gases (fermions, bosons, light, sound, magnetic moments) qualitatively and quantitatively, in the classical and quantum limits;
8. expound the basic properties of phase transitions of the first and second kind, with qualitative and quantitative application to gas liquefaction and ferromagnetism within the van der Waals and Weiss approaches, respectively;
9. explain the physical causes and mutual relationships of fluctuations, dissipation, and macroscopic irreversibility.
1. Thermodynamics as an autonomous discipline
1.1. Introduction. Basic concepts.
1.2. First law. Engines.
1.3. Second law. Reversibility and entropy.
1.4. Thermodynamic potentials.
1.5. Practical calculations.
2. Introduction to statistical physics
2.1. Basic considerations.
2.2. The ensemble as a universal random model.
2.3. Connection with thermodynamics.
3. Canonical and grand canonical ensembles
3.1. Canonical ensemble.
3.2. Grand canonical ensemble.
3.3. Sums over states as generating functions.
3.4. Classical ideal gas.
3.5. Maxwell distribution and equipartition of energy.
4. Quantum statistical physics
4.1. Basic considerations.
4.2. Ideal fermion gas.
4.3. Ideal boson gas.
4.4. Practical calculations in a finite system.
5. Examples and models
5.1. Barometric formula.
5.2. Chemical reactions.
5.3. Two-atom molecules.
5.4. Magnetic fields.
5.6. Heat capactity of crystals.
5.7. Van der Waals model of gas liquefaction.
5.8. Macroscopic analysis of stability.
6. Fluctuation and non-equilibrium processes
6.1. Brownian motion.
6.2. Thermodynamic fluctuations.
6.3. Wiener-Khintchine theorem.
6.4. Nyquist theorem.
6.5. Return to equilibrium as an irreversible process.
REQUIREMENTS FOR STUDENTS:
Students should pass four out of six tests spread out during the course.
GRADING AND ASSESSING THE WORK OF STUDENTS:
Students are admitted to an oral examination if they have passed a written one. They are admitted to the written examination if they have passed four out of six above-mentioned tests. If they have passed all tests with grade 4 or 5, the grade in the written examination is increased by one.
- C. Kittel, Elementary Statistical Physics, Dover 2004, ISBN 0486435148.
- R. Kubo et al., Statistical mechanics: an advanced course with problems and solutions, North-Holland, Amsterdam 1988, ISBN 0444871039
- Skripta: http://www.phy.hr/dodip/notes/statisticka.html