
Course unit
PHYSICS OF COMPLEX SYSTEMS
SCP7081763, A.A. 2019/20
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 
FIS/03 
Material Physics 
6.0 
Course unit organization
Period 
First semester 
Year 
2nd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Prerequisites:

Students are expected to already know the main concepts of equilibrium statistical mechanics, including phase transition, critical exponents and the renormalization group. 
Target skills and knowledge:

The students are expected to acquire the knowledge of selected topics in the physics of complex systems, including non equilibrium statistical mechanics, and the ability to understand the current scientific literature on related subjects. 
Examination methods:

Oral examination covering three or four of the topics chosen by the teacher among all those treated in the course. To each topic ample time is devoted to the exposition and to the discussion of possible connections with other parts of the program. This allows to ascertain how the student masters the subject. 
Assessment criteria:

The exam will assess the knowledge gained by the student with respect to the topics taught in the course, and his/her ability in general understanding and in critical thinking, also in connecting different topics in the course subjects. 
Course unit contents:

Introduction to the physics of complexity and of emergent phenomena (general points of view of P.W. Anderson, N. Goldenfeld, L.P. Kadanoff, ...)
Brief overview of Brownian motion, stochastic differential equations and stochastic processes.
Statistical mechanics out of equilibrium: microscopic reversibility and macroscopic irreversibility.
Detailed balance in equilibrium. Linear response theory and transport phenomena.
Onsager reciprocity relations with examples (Seebeck and Peltier effects, etc.)
Fluctuationresponse theorem, dynamic susceptibility and fluctuationdissipation theorem. KramersKronig relations. Microscopic basis of Brownian motion.
Thermodynamics out of equilibrium at the micro and nanoscales. Markovian description of nonequilibrium dynamics. Fluctuation theorems and work identities. Generalized detailed balance. Entropy production.
Outofequilibrium phase transitions. Directed percolation. Asymmetric simple exclusion and
related processes, some basic results. Theory of large deviations. Molecular motors. Applications of GallavottiCohen theorem.
Stochastic dynamics of surfaces and interfaces: the KardarParisiZhang equation.
Computational complexity and information theory. The random energy model and the random code ensemble. Complex energy landscapes and reweighting methods. 
Planned learning activities and teaching methods:

Frontal lectures mainly using the blackboard 
Textbooks (and optional supplementary readings) 

R. Livi and P. Politi, Non Equilibrium Statistical Physics: A Modern Perspective. : Cambridge University Press, 2017.

M. Mezard and A. Montanari, Information, Physics and Computation. : Oxford University Press, 2009.


