
Course unit
STATISTICAL MECHANICS OF COMPLEX SYSTEMS
INP5070381, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
FIS/03 
Material Physics 
9.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
9.0 
72 
153.0 
No turn 
Prerequisites:

Good knowledge of mathematical analysis, calculus and basic physics.
For "Physics of Data" students the course has 6 CFU. However, if they are not adequately trained in statistical mechanics, they are encouraged to follow all 9 credits 
Target skills and knowledge:

The purpose of the course is to provide the student with a wide vision on how theoretical physics can contribute to understand phenomena in a variety of fields ranging from subjects like system in thermodynamic equilibrium and out of equilibrium, diffusion processes, and, more in general, to the physics of complex systems. Particular emphasis will be placed on the relationships between different topics allowing for a unified mathematical approach where the concept of universality will play an important role. The course will deal with a series of paradigmatic physical systems that have marked the evolution of statistical physics in the last century.
Each physical problem, the modeling and the solution thereof, will be described in detail using powerful mathematical techniques.
Outcomes
A student who has achieved the objectives of the course will have the ability to: propose minimal models of natural / complex systems based on empirical data and inspired by the statistical mechanics;
Solve the models using exact and approximate analytical methods and predict behavior that can be verified experimentally or by accurate and sophisticated data analysis;
Understand the predictions of models in terms of phases, phase transitions, scaling laws. 
Examination methods:

The first part of the verification of the acquired knowledge will evaluate the homework exercises and the participation of the students in the class discussions The second part will takes place through, a common written test with 12 exercises to be solved and open questions to test the knowledge on basic concepts, the scientific vocabulary, the ability to synthesis and critical discussion acquired during the course. The third part is oral, optional and it will be based on a discussion on the various topics of the course. 
Assessment criteria:

The criteria used to verify the knowledge and skills acquired are:
1) understanding of the topics covered;
2) critical ability to connect the acquired knowledge;
3) completeness of the acquired knowledge;
4) synthesis ability;
5) understanding of the terminology used
6) ability to use the analytical methodologies and computational techniques illustrated during the course to solve or at least to approach set problems on complex systems where statistical mechanics plays an important role. 
Course unit contents:

The program can be summarized as follows
Statistical mechanics and Entropy
Ising model
Diffusion Processes
Complex networks.
Principle of maximum entropy and inference
Montecarlo simulations
Dynamics of and on networks.
Percolation on networks.
Neural networks 
Planned learning activities and teaching methods:

The course is organized in lectures whose contents are presented on the blackboard, sometimes with the help of images, diagrams and videos. The teaching is interactive, with questions and presentation of case studies, in order to promote discussion and critical thinking. 
Additional notes about suggested reading:

Beside some suggested books, materials (notes and published papers) will be available to the students in Moodle.
Sethna, James. Statistical mechanics: entropy, order parameters, and complexity. Vol. 14. Oxford University Press, 2006.
Lecture notes. 
Textbooks (and optional supplementary readings) 

J. P. Sethna, Entropy, Order Parameters and Complexity. : Oxford, 2015.

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem based learning
 Interactive lecturing
 Working in group
 Questioning
 Problem solving
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Mathematica
 Matlab

