First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCP7081763, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course Second cycle degree in
SC2382, Degree course structure A.Y. 2017/18, A.Y. 2019/20
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Degree course track PHYSICS OF MATTER [002PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination PHYSICS OF COMPLEX SYSTEMS
Website of the academic structure
Department of reference Department of Physics and Astronomy
E-Learning website
Mandatory attendance No
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge ANTONIO TROVATO FIS/03

ECTS: details
Type Scientific-Disciplinary 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 of
Individual study
Lecture 6.0 48 102.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2017 course timetable

Examination board
Board From To Members of the board
2 PHYSICS OF COMPLEX SYSTEMS 01/10/2019 30/11/2020 TROVATO ANTONIO (Presidente)
ORLANDINI ENZO (Membro Effettivo)
1 PHYSICS OF COMPLEX SYSTEMS 01/10/2018 30/11/2019 STELLA ATTILIO (Presidente)
ORLANDINI ENZO (Membro Effettivo)

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.)
Fluctuation-response theorem, dynamic susceptibility and fluctuation-dissipation theorem. Kramers-Kronig relations. Microscopic basis of Brownian motion.

Thermodynamics out of equilibrium at the micro- and nano-scales. Markovian description of non-equilibrium dynamics. Fluctuation theorems and work identities. Generalized detailed balance. Entropy production.

Out-of-equilibrium phase transitions. Directed percolation. Asymmetric simple exclusion and
related processes, some basic results. Theory of large deviations. Molecular motors. Applications of Gallavotti-Cohen theorem.

Stochastic dynamics of surfaces and interfaces: the Kardar-Parisi-Zhang 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. Cerca nel catalogo
  • M. Mezard and A. Montanari, Information, Physics and Computation. --: Oxford University Press, 2009. Cerca nel catalogo