99512 - STATISTICAL PHYSICS FOR CLIMATE SCIENCE

Conoscenze e abilità da conseguire

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.

Contenuti

• 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

Testi/Bibliografia

S. Ross, ntroduction 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.

Metodi didattici

The course is divided into 2 modules of 24 hours each.

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

Modalità di verifica e valutazione dell'apprendimento

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.

Strumenti a supporto della didattica

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

Orario di ricevimento

Consulta il sito web di Elisa Ercolessi

Consulta il sito web di Marco Lenci