
Course unit
STATISTICAL MECHANICS OF COMPLEX SYSTEMS
INP7081057, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
MAT/07 
Mathematical 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 
Examination board
Board 
From 
To 
Members of the board 
5 2019 
01/10/2019 
15/03/2021 
MARITAN
AMOS
(Presidente)
SUWEIS
SAMIR SIMON
(Membro Effettivo)
AZAELE
SANDRO
(Supplente)

4 2018 
01/10/2018 
15/03/2020 
MARITAN
AMOS
(Presidente)
SUWEIS
SAMIR SIMON
(Membro Effettivo)
SENO
FLAVIO
(Supplente)

3 2017 
01/10/2017 
15/03/2019 
MARITAN
AMOS
(Presidente)
SUWEIS
SAMIR SIMON
(Membro Effettivo)
SENO
FLAVIO
(Supplente)

Prerequisites:

Good knoledge of mathematical analysis, calculus and basic physics. 
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 met the objectives of the course will have a practical knowledge of:
• Models of statistical mechanics of natural systems
• Complex networks
• Diffusion processes
The student will have the appropriate knowledge and the correct predisposition to face and solve problems of various kinds with models that capture the essential ingredients. 
Examination methods:

Final examination based on: Written and oral examination and weekly exercises proposed during the course 
Assessment criteria:

Critical knowledge of the course topics.Ability to present the studied material. Discussion of the student project. 
Course unit contents:

1. Equilibrium statistical mechanics, the principle of maximum
entropy, statistical ensemble, derivation of thermodynamics, paradigmatic models of statistical mechanics, mean field theory, critical phenomena and scaling.
2. Fractal geometry with applications to the natural forms of many systems (for example transportation networks, river basins).
3. Scaling theory and its use in physics, ecology, biology.
4. Nonequilibrium statistical mechanics, Brownian motion/diffusion, Markov processes, Langevin equation and the FokkerPlanck, linear response theory. Applications to biology, ecology and human mobility / traffic.
5. Graph theory with application to architecture ecological, biological and food trade networks. 
Planned learning activities and teaching methods:

Lecture supported by tutorial, assignment, analytical and numerical problems 
Additional notes about suggested reading:

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.


