Statistical Thermodynamics

Physics, First Cycle
Educational Physics
2 year
first or second
Course director:
Lecturer (contact person):
Hours per week – 1. or 2. semester:

Enrollment in year 2.

Physics 1, Physics 2, Mathematics 1, and Mathematics 2.

Passed problem-solving examination is a prerequisite for the theoretical part of the examination.

Content (Syllabus outline)

Thermodynamic variables, thermodynamic equilibrium, equation of state. First law of thermodynamics, work. Second law of thermodynamics, reversibile and irreversible changes, heat engine. Entropy of pure substances. Thermodynamic potentials, Maxwell relations. Phase transitions. Transport phenomena.
Statistical physics:
Phase space, probability density. Microcanonical distribution, canonical distributions, temperature, average energy, energy fluctuations, equipartition theorem. Equation of state, virial expansion. Gibbs and Boltzmann entropy. Quantum canonical distribution. Harmonic oscillator, rotator, diatomic molecule. Paramagnetism, Ising model, Debye model. Grand canonical distribution, grand potential; Fermi-Dirac and Bose-Einstein distributions. Electrons in metal. Kinetic theory of gases.


Kuščer in S. Žumer, Toplota. DMFA, Ljubljana, 1987.
W. Greiner, L. Neise in H. Stoecker, Thermodynamics and Statistical Mechanics. Springer, Berlin, 1995.
D. Chandler, Introduction to Modern Statistical Mechanics. Oxford University Press, Oxford, 1987.
D. C. Mattis, Statistical Mechanics Made Simple. World Scientific, Singapore, 2003.
R. Baierlein, Thermal Physics. Cambridge University Press, Cambridge, 1999.
F. Schwabl, Statistical Mechanics. Springer, Berlin, 2002.
C. Hermann, Statistical Physics. Springer, New York, 2005.
L. D. Landau in E. M. Lifshitz, Statistical Physics I. Pergamon, Oxford, 1980.
P. Ziherl in G. Skačej, Rešene naloge iz termodinamike. DMFA, Ljubljana, 2005.
G. Skačej in P. Ziherl, Rešene naloge iz statistične fizike.  DMFA, Ljubljana, 2005.

Objectives and competences

Consolidation of understanding of the laws of thermodynamics and a systematic definition of thermodynamic potentials as the general formalism of thermodynamics. Overview of foundations of equilibrium statistical physics as the microscopic theory of matter and fields.

Intended learning outcomes

Knowledge and understanding:
Understanding of laws of thermodynamics and the theoretical concepts of generalized forces and coordinates, work, and thermodynamic potentials. Understanding of the meaning and the role of thermodynamic description of systems. Command of methods of statistical physics, understanding of concepts of phase space and phase integral, temperature, and chemical potential.

Students will learn to recognize, define, and solve problems in equilibrium thermodynamics and statistical physics.

The course provides an insight into the dual nature of physics as an empirical science including a phenomenological description of macroscopic systems derived from a microscopic interactions between the constituents of matter. The agreement and complementarity of the two approaches emphasize the importance of description of physical systems more than one scale.

Transferable skills:
Many examples and problems in thermodynamics and statistical physics involve several mutually dependent phenomena or are difficult to solve analytically. An important objective of the course is to show how to identify the dominant and the subdominant aspects of a given phenomenon and how to solve problems approximately, thereby simplifying the analysis.

Learning and teaching methods

Lectures, tutorials, homework problems, consultations.


2 written tests (mid-term and end-term) applied towards the problem-solving examination, problem-solving examination
Theoretical examination
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

P. Ziherl and R. D. Kamien, Maximizing entropy by minimizing area: Towards a
new principle of self-organization, J. Phys. Chem. B 105, 10147 (2001).
M. A. Glaser, G. M. Grason, R. D. Kamien, A. Košmrlj, C. D. Santangelo, and P.
Ziherl, Soft spheres make more mesophases, Europhys. Lett. 78, 46004
N. Osterman, D. Babić, I. Poberaj, J. Dobnikar, and P. Ziherl, Observation of
condensed phases of quasi-planar core-softened colloids, Phys. Rev. Lett. 99,
248301 (2007).
A. Hočevar and P. Ziherl, Degenerate polygonal tilings in simple animal tissues,
Phys. Rev. E 80, 011904 (2009).
A. Košmrlj, G. J. Pauschenwein, G. Kahl, and P. Ziherl, Continuum theory for
cluster morphologies of soft colloids, J. Phys. Chem. B 115, 7206 (2011).