ELEMENTS OF STATISTICAL PHYSICS AND INFORMATION THEORY
Academic Year 2025/2026 - Teacher: Giuliano CHIRIACO'Expected Learning Outcomes
The course introduces the concepts and theoretical background of statistical physics, using an information Theory approach. The course also lays the foundation for understanding fundamental concepts of quantum information theory and thermodynamics, topics currently of great fundamental and applied interest, which students will be able to explore in greater depth in subsequent courses.
- Knowledge and Understanding – Knowledge of the main theoretical ideas and techniques used in statistical physics. Knowledge of some basic numerical techniques using the Mathematica-Wolfram software.
- Applying Knowledge and Understanding – Ability to solve problems by applying theoretical techniques and approximations to the analysis/simulation of systems of interest to statistical mechanics.
- Marking Judgments – Ability to make choices during the course and thesis, and to argue interpretations of physical phenomena.
- Communication skills – Communication skills in the field of statistical physics and information theory, to be developed by preparing the expository part of the exam.
- Learning skills – Acquisition of cognitive tools for continuous updating of knowledge in the field, through access to computer labs and specialized literature, and during the preparation of the expository part of the exam.
Course Structure
Classroom lessons (6 credits, 42 hours).
Information for students with disabilities and/or learning disabilities.
To ensure equal opportunities and in compliance with applicable laws, interested students may request a personal interview to plan any compensatory and/or dispensatory measures, based on their learning objectives and specific needs. Students may also contact the CInAP (Center for Active and Participatory Integration - Services for Disabilities and/or Learning Disabilities) contact teacher in the Department of Physics.
Information for students with disabilities and/or learning disabilities.
To ensure equal opportunities and in compliance with applicable laws, interested students may request a personal interview to plan any compensatory and/or dispensatory measures, based on their learning objectives and specific needs. Students may also contact the CInAP (Center for Active and Participatory Integration - Services for Disabilities and/or Learning Disabilities) contact teacher in the Department of Physics.
Required Prerequisites
Classical mechanics, analytical mechanics, linear algebra, mathematical analysis, mathematical methods, notes on quantum mechanics and the structure of matter (the necessary concepts will be introduced in the course).
Attendance of Lessons
Attendance at the course is strongly recommended as per the Course Regulations.
Detailed Course Content
- Preliminary notions: Purpose of statistical mechanics. Managing incomplete knowledge. Elements of kinetic theory and classical transport. Liouville equation, distribution function, Boltzmann kinetic equation, theorem H. Concept of information: definition, information associated with a discrete and continuous probability.
- Classical Statistical Mechanics: Constants of motion and thermal equilibrium. Principle of maximum missing information. Existence and uniqueness of the solution. Microcanonical ensemble, application examples. Constrained information, canonical and grand canonical ensemble. Application examples. Equipartition of energy in linear systems. Discrete systems: paramagnets, impurities, the Ising model, and phase transitions. Paramagnets. Chemical reactions.
- Quantum Statistical Mechanics: equilibrium. Density matrix. Principle of maximum information. Distinguishable particles: spin systems and applications to quantum computers. Identical particles, ideal quantum gas in second quantization (grand canonical approach). Fermi gases in solids, Pauli paramagnetism. Bosons: phonons and specific heat, photons, and Bose-Einstein condensation.
- Non-equilibrium statistical mechanics. Transport, currents, and thermodynamic forces, transport coefficients, Onsager relations, thermoelectricity. Continuity equations in equilibrium and out of equilibrium. Boltzmann kinetic equation in the relaxation-time approximation. Application examples.
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.
[2] Carlo Di Castro e Roberto Raimondi, Statistical Mechanics and Applications in Condensed Matter, Cambridge University Press, 2015.
[3] K. Huang, Introduction to Statistical Physics, Chapman & Hall, 2010.
[4] D. Arovas, Lecture Notes on Thermodynamics and Statistical Mechanics (A Work in Progress), available on line, 2019.
[4] D. Arovas, Lecture Notes on Thermodynamics and Statistical Mechanics (A Work in Progress), available on line, 2019.
[5] C. Kittel, Elementary Statistical Physics, Wiley&Sons (1958).
[6] M. Kardar, Statistical Physics of Particles, Cambridge University Press (2007).
[7] Stephen Wolfram, An Elementary Introduction to the Wolfram Language, Cambridge University Press, 2015.
[6] M. Kardar, Statistical Physics of Particles, Cambridge University Press (2007).
[7] Stephen Wolfram, An Elementary Introduction to the Wolfram Language, Cambridge University Press, 2015.
[8] G. Mussardo, Statistical Field Theory: an Introduction to Exactly Solved Models in Statistical Physics, Oxford University Press (2020).
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Preliminary Notions | |
| 2 | Classical Statistical Mechanics | |
| 3 | Quantum Statistical Mechanics | |
| 4 | Non-equilibrium statistical physics |
Learning Assessment
Learning Assessment Procedures
- The standard exam includes a written test (which may be replaced with ongoing tests) and an oral exam, in which the written exam exercises will be discussed and questions on course topics will be asked.
- At the student's request and subject to the instructor's approval, the written exam may be replaced by a paper that includes an analytical or numerical calculation that the student must develop independently but with guidance, based on the recommended texts and any review articles recommended by the instructor. In this case, Part (b) will be expository.
- The oral exam is evaluated taking into account: (1) relevance of the answers to the questions asked; (2) level of understanding of the content presented; (3) accuracy in presenting the calculations; (4) ability to connect with other topics in the course (or previous courses) and to provide examples; (5) command of language and clarity of presentation.
- Information for students with disabilities and/or learning disabilities (LDs): To ensure equal opportunities and in compliance with applicable laws, interested students may request a personal interview to plan any compensatory and/or dispensatory measures, based on their educational objectives and specific needs. Students may also contact our Department's CInAP (Center for Active and Participatory Integration - Services for Disabilities and/or LDs) contact, Professor Catia Petta.
Examples of frequently asked questions and / or exercises
All course topics may be the subject of exam questions. The following are some examples (not exhaustive).
- Grand Canonical Ensemble in Quantum Mechanics. Fermi-Dirac Distribution.
- Sommerfeld Model in Metals: Concept of Density of States and Derivation of Typical Scales.
- Specific Heat of Metals: Classical Theory and Its Inadequacy. Gibbs Paradox.
- Thermodynamic Potentials: Definitions, Use, and Connection to Statistical Mechanics.
- Derivation of the Shannon Formula for Discrete Probability Distributions.
- Phonons and Specific Heat.
- Specific Heat of Insulators: Classical Theory and Its Inadequacy. Gibbs Paradox.
- Bose-Einstein Condensation
- Uniqueness of the Classical Equilibrium Distribution Derived from the Maximum Information Principle (Canonical Ensemble)
- Relationship between Missing Information and Thermodynamic Entropy.
- Partition function for classical linear problems and equipartition theorem.
- Grand Canonical Ensemble in Quantum Mechanics. Fermi-Dirac Distribution.
- Sommerfeld Model in Metals: Concept of Density of States and Derivation of Typical Scales.
- Specific Heat of Metals: Classical Theory and Its Inadequacy. Gibbs Paradox.
- Thermodynamic Potentials: Definitions, Use, and Connection to Statistical Mechanics.
- Derivation of the Shannon Formula for Discrete Probability Distributions.
- Phonons and Specific Heat.
- Specific Heat of Insulators: Classical Theory and Its Inadequacy. Gibbs Paradox.
- Bose-Einstein Condensation
- Uniqueness of the Classical Equilibrium Distribution Derived from the Maximum Information Principle (Canonical Ensemble)
- Relationship between Missing Information and Thermodynamic Entropy.
- Partition function for classical linear problems and equipartition theorem.