FIS/02 - 6 CFU - 2° Semester

Teaching Staff

Email: gfalci@dmfci.unict.it
Office: Dipartimento di Fisica e Astronomia, Città Universitaria, Ufficio 212
Phone: 0953785337
Office Hours: Lunedi 18:00-20:00 (ex DMFCI), Mercoledi 10:30-11:30 (DFA)

Learning Objectives

The course introduces concepts of statistical mechanics and the necessary theoretical background. We adopt the Information Theoretical approach with a unified treatment of classical and quantum statistics. The course also provides the basis for the understanding of concepts in quantum information and quantum thermodynamics. Both are timely topic from the fundamental point of view and for applications, which students will encounter in their subsequent studies.

Course Structure

Detailed Course Content

  1. Preliminary concepts Goal of statistical mechanics. Handling incomplete information. Elements of kinetic theory and classical transport. Informazione: definition, information associated with a probability (discrete and continuous). Thermodynamics: from principles to thermodynamic potentials.
  2. Classical Statistical mechanics: equilibrium Canonical formalism. Past, future and irreversibility. Conserved quantities and thermal equilibrium. Principle of maximal (missing) information. Existence and unicity of the solution. Relation with thermodynamics: temperature, adiabatic theorem, work and heat, ideal thermal machines. Equipartition theorem in linear systems. Gibbs paradox. Paramagnets. Gran-canonical ensemble.
  3. Quantum Statistical mechanics: equilibrium Density Matrix. Principle of maximal information. Distinguishable particles: spin systems and quantum computers. Identical particles, ideal quantum gas in second quantization (grand canonical). Fermi gas and metals. Bosons: phonons and specific heat, photons and Bose-Einstein condensation.
  4. Selected topic (only one!) -- Physical basis of the postulates: statistical ensembles, decoherence. Small deviations from equilibrium: Onsager relations, Einstein relation, fluctuation-dissipation theorem. Nonequilibrium: Boltzmann equations and H theorem. Jarzynski relation and Crooks fluctuation theorem.

Textbook Information

[1] Amnon Katz, Principles of Statistical, Mechanics. The Information Theory Approach, Freeman, San Francisco, 1967
[2] Carlo Di Castro e Roberto Raimondi, Statistical Mechanics and Applications in Condensed Matter, Cambridge University Press, 2015.
[3] G. Falci, Lecture notes on Statistical Physics and Information Theory, 2020.
[4] D. Arovas, Lecture Notes on Thermodynamics and Statistical Mechanics (A Work in Progress), available on line, 2019.
[5] K. Huang, Introduction to Statistical Physics, Chapman & Hall, 2010.
[6] Stephen Wolfram, An Elementary Introduction to the Wolfram Language, Cambridge University Press, 2015.
[7] G. Baumann, Mathematica for Theoretical Physics, Springer, 2005.

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