First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SC02121365, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2016/17

Information on the course unit
Degree course Second cycle degree in
SC1171, Degree course structure A.Y. 2014/15, A.Y. 2017/18
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Degree course track Common track
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
Mandatory attendance No
Language of instruction Italian
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 ATTILIO STELLA FIS/02

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines FIS/02 Theoretical Physics, Mathematical Models and Methods 6.0

Mode of delivery (when and how)
Period First semester
Year 2nd Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
Hours of
Individual study
Lecture 6.0 48 102.0 No turn

Start of activities 02/10/2017
End of activities 19/01/2018

Examination board
Board From To Members of the board
5 Fisica dei Sistemi Complessi 01/10/2017 30/11/2018 STELLA ATTILIO (Presidente)
ORLANDINI ENZO (Membro Effettivo)

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, ...)

Selected topics in the statistics of polymers, percolation,
fractals, and disorder. Continuous symmetries and Kosterliz Thouless transition.

Brownian motion. Mathematics of Brownian motion and
stochastic differential equations. Stochastic processes.
Statistical mechanics out of equilibrium.
Microscopic reversibility and macroscopic irreversibility.
Detailed balance in equilibrium. Onsager reciprocity relations
with examples (Seebeck and Peltier effects, etc.).
Fluctuation-response theorem, dynamic susceptivity 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. Asymmetric simple exclusion and
related processes, some basic results. Theory of large deviations.
Molecular motors. Applications of Gallavotti-Cohen theorem.
Textbooks (and optional supplementary readings)