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

• • Elements of Probability for Applications (24 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.

  Elements of stochastic processes: stationarity; i.i.d. random variables; Markov chains.

  • Statistical Models for Physics (24 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 microcanocical ensemble and entropy; the canonical ensemble: partition function, free energyother tjhermodynamic potentials; the generalised equipartition theorem.

  Applications: The (non relativistic) deal gas; the ultra-relativist perfect gas; a system of harmonic oscillators; a gas in the gravitational fileld

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 2 modules of 24 hours each.

Classes will consists in front lectures on theory, applications and exercises.

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 to be familiar and have a good understanding of the different subjects.

The organization of the presentation and a rigorous scientific language will be also considered for the formulation of the final grade.

The “cum laude” honor is granted to students who demonstrate a personal and critical rethinking of the subject.

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