87997 - PHYSICS OF COMPLEX SYSTEMS

Scheda insegnamento

Anno Accademico 2020/2021

Conoscenze e abilità da conseguire

At the end of the course the student will have the basic knowledge of Complex Systems Physics with application to biological and social systems. He/she will acquire theoretical tools to analyze, predict and control the evolution of models, including: - statistical physics and dynamical system theory of complex systems; - dynamics of systems on network structures; - stochastic thermodynamics; - stochastic dynamical systems.

Contenuti

Definition of complex systems and introduction to Complex Systems Physics

The problem of Modeling a complex system: different tipologies of models according to the different description scales of the considered phenomenon, discrete and cotinuous models, deterministic and stochastic models, definition of control parameters, thermodynamic limit, emergent properties, introdution critical phenomena and phase transitions, comparison with experimental observations and the validation problem. Examples of complex sytems in Physics, Biology and Social systems.

Mathematical methods for complex systems

Introduction to dynamical systems theory, averaging principle and ergodic theory, chaotic systems and definition attractors. Stochastic dynamical systems and elements of probability theory. Random walks, Markov processes and diffusion processes. Wiener process and stochastic differential equations. Chapman-Kolmogorov equation, Stochastic Liouville equation and Fokker-Planck equations. Central limit theorem, definition of Levy flights and power law distributions. Basic notions of spectral theory for random matrices.

Introduction to non-equilibrium statistical physics

Background of Classical Statistical Mechanics: Maxwell-Bolzmann distribution, Maximum Entropy Principles and their relation withShannon information theory. Discrete Markov models and Statistical Mechanics, stationary versus equilibrium states,reversible and irreversible processes, detailed balance condition entropy production and irreversibility, introduction to Kolmogorov-Sinai entropy for Markov systems. Fluctuations in systems at equilibrium, Onsager reciprocity relations phase transitions and self-organized criticalities in complex systems.

Dynamical Systems on Networks:

definition of networks and introduction to their topological properties, networks as models of complex interactions, free scale networks and power law distributions, random walks on networks, model for traffic dynamics and effects nonlinear interaction (congestion transition), spectral properties of Laplacian and Stochastic matrices.

 

Testi/Bibliografia

Materials and notes provided by the professor

Gregoire Nicolis, Catherine Nicolis Foundations of Complex Systems Nonlinear Dynamics, Statistical Physics, Information and Prediction World Scientific, 3 set 2007

Yaneer Bar-yam Dynamics Of Complex Systems Perseus Books Cambridge, MA, USA ©1997

Nino Boccara "Modeling Complex Systems" Graduate Text in Contemporary Physics, Springer, 2004
Per Bak "How Nature Works: The Science of Self-Organised Criticality" New York, NY: Copernicus Press, 1996

N. G. Van Kampen, Stochastic Processes in Physics and Chemistry. Elsevier, 2007.

Other Reference texts


K. Huang "Statistical Mechanics" ISBN: 978-0-471-81518-1, 1988

Complex Systems and Networks Dynamics, Controls and Applications Editors: Lu, J., Yu, X., Chen, G., Yu, W. (Eds.) Springer 2016

Roberto Livi, Paolo Politi, Nonequilibrium Statistical Physics A Modern Perspective cambridge university press 2017

Metodi didattici

Frontal lessons and exercises

Modalità di verifica dell'apprendimento

In deep analysis of a subject among those discussed in the course by a short thesis and computer simulations

Strumenti a supporto della didattica

use of computer for model simulations

Orario di ricevimento

Consulta il sito web di Armando Bazzani