99512 - STATISTICAL PHYSICS FOR CLIMATE SCIENCE

Learning outcomes

At the end of the course, the student will have a basic knowledge of theoretical concepts and methods of statistical physics, including: the probabilistic laws that rule the microscopic description for modeling the behaviour of thermodynamic and complex systems; description of systems at equilibrium; an approach to dynamics and non equilibrium physics. The student will be able to describe the main theoretical concepts and tools in order to use them to solve -analytically or with the aid of numerical simulations- simple but paradigmatic models, with applications to different branches of physics and in particular to problems of climate science.

Course contents

The course is organized in two modules, offering an introduction to the fundamentals of the theory of probability and the basics of statistical physics.

• Elements of Probability for applications (28 h, Prof. Marco Lenci)

Mathematical foundations of probability: probability spaces, events; conditional probability, independence; Bayes’ Theorem.

Random variables: general theory; discrete and continuous random variables; moments; important examples and applications; joint distribution.

Limit theorems: law of large numbers, characteristic function, Central Limit Theorem, moment-generating function.

• Statistical Models for Physics (28 h, prof. Elisa Ercolessi)

Thermodynamics and its microscopic interpretation: work, heat, entropy; the laws of thermodynamics and thermodynamic potentials; Kinetic theory of gases.

Introduction to classical statistical mechanics: the state of a system of many particles; the microcanonical ensemble and entropy; the canonical ensemble: partition function, free energy and other thermodynamic potentials; the generalised equipartition theorem.

Applications: The non relativistic odeal gas; the ultra-relativistic perfect gas; a system of harmonic oscillators; a gas in the gravitational field.

 

Readings/Bibliography

S. Ross, Introduction to Probability Models, 12th Ed. (Academic Press)

Greiner et al, Thermodynamics and Statistical Mechanics (Springer)

Huang, Statistical Mechanics (John Wiley & Sons).

Further reading suggestions and other didactic materials will be made available in the Virtuale platform.

Teaching methods

The course is divided into two modules of 28 hours each, consisting of front lectures on theory, applications, and exercises.

In the second module, part of the lectures will be used for guided discussions among students and/or with the teacher, and for solving exercises in small groups of peers.

Assessment methods

A 3-hour written exam consisting of problems and theory questions on both the Probability and the Statistical Physics parts of the course.

Students should demonstrate familiarity with and have a good understanding of the different subjects.

The final grade is the result of an average of the grades of the two parts, evaluated according to the following scheme:

Grade 18-19: basic knowledge and ability to analyze only a very limited number of topics covered in the course; overall correct language.

Grade 20-25: discrete knowledge and ability to analyze only a limited number of topics covered in the course; overall correct language.

Grade: 26-28: good knowledge and ability to analyze a large number of topics covered in the course; mastery of scientific language and correct use of specific terminology.

Grade: 29-30: comprehensive preparation on the topics covered in the course, showing a very good/excellent knowledge and ability analysis; mastery of scientific language and correct use of specific terminology.

The “cum laude” honor is granted to students who demonstrate the ability to organize comparative analyses and personal/critical rethinking of the subject.

Students with Specific Learning Disabilities (SLD) or temporary/permanent disabilities are advised to contact the University Office responsible in a timely manner (https://site.unibo.it/studenti-con-disabilita-e-dsa/en ). The office will be responsible for proposing any necessary accommodations to the students concerned. These accommodations must be submitted to the instructor for approval at least 15 days in advance, and will be evaluated in light of the learning objectives of the course.

Teaching tools

Additional notes and exercises; available to download from the university repository Virtuale.

Office hours

See the website of Elisa Ercolessi

See the website of Marco Lenci