## Trinity College Dublin, The University of Dublin

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# Module MAU34405: Statistical Physics I

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2019-20
Lecturer
Prof Manuela Kulaxizi
Contact Hours
• 3 hours per week - lectures and problem solving under lecturer's supervision.
• 1 hour per week - problem solving tutorial, devoted mostly to solution of home works.

Course Outline

In this course we will study macroscopic systems, i.e. systems that consist of very large number of smaller ones. Because of the large number of components, they acquire new significant properties which do not exist on the level of single particles. The main such property is existence of the function called entropy and of the second law of thermodynamics which states that entropy always increases. Our main goal would be to master these concepts and understand how they emerge from the microscopic description, i.e. from classical or quantum mechanics, when it is applied to the system with very large number of components. On the way we will learn a lot of interesting math, encounter several exciting physical phenomena.

Module Content
The detailed syllabus and tentative schedule are given here , only the key elements are listed below;
• Thermodynamics: 0th,1st,2nd,3rd laws. Concept of temperature and entropy.
• Thermodynamic potentials: Ideal gases. Heat engines. Reversible vs irreversible processes.
• Calculus: Gauss integrals. Gamma function (generalisatin of factorial). Saddle-point approximation. Euler-Maclaurin resummation.
• Certain elements of cominatorics and probability theory.
• Foundations of statistical physics. Probabilistic description of statistical systems. Microcanonical, canonical, and grand canonical ensembles. Partition function. Derivation of thermodynamics from statistical physics. Boltzmann and Gibbs approaches to entropy.
• Applications of thermodynamics and statistics in physical systems.

• Any standard book, to use for background reading, there is no shortage of choices. E.g: Kerson Huang, 'Introduction to Statistical Physics'
• L.D. Landau, E.M. Lifshitz, 'Statistical Physics' (good to read starting from December and later on as MA3444 follow-up)
Module Prerequisite

MAU23402

Assessment Detail

This module will be examined in a 2-hour examination in Michaelmas term. The continuous assessment contributes 20% to the final annual mark. Re-assessments if required will consist of 100% exam.