- Docente: Armando Bazzani
- Credits: 6
- SSD: MAT/07
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Physics (cod. 9244)
-
from Sep 15, 2025 to Dec 16, 2025
Learning outcomes
Basic knowledge of physical and mathematical methods to develop dynamic and statistical model for the study of complex systems.
Course contents
Main objective: introduction to the Physics of Complex Systems, definition of the complexity concept and emergent properties.
The role of models in Physics: concept of dynamical system, linear dynamical systems and their integration, elements of control theory, integrable and chaotic systems, Ljapunov exponents and the concept of predictivity.
Central limit theorem and introduction to stochastic dynamical systems: properties of discrete Markov processes, concept of entropy and entropy production, equilibria in detailed balance and stochastic reversibility, Maximum Entropy Principles.
Definition of a complex system model and role of interactions and use of complex networks to classify the interaction structure.
Examples for applications of dynamical systems to the complex systems physics.
Discrete stochastic systems and physical applications.
Introduction to statistical mechanics: concept of emergent properties, critical states and phase transitions.
Study of empirical distributions obtained from big data of complex systems: exponential laws and power law distributions.
Analytical and numerical methods for the study and validation of a stochastic dynamical model for the simulation of complex systems.
Examples of models for Complex Systems Physics with applications to chemistry, biology, economics and social systems.
Example of emergent properties: phase transitions, synchronization, soliton formation, reaction diffusion models.
Readings/Bibliography
papers and materials provided during the course
G.Nicolis C.Nicolis FOUNDATIONS OF COMPLEX SYSTEMS
Nonlinear Dynamics, Statistical Physics, Information
and Prediction World Scientific 2007
Luca Leuzzi, Enzo Marinari, Giorgio Parisi Probability Theory for Quantitative Scientists Cambridge 2025
Nino Boccara Modeling Complex Systems Springer 2010
Teaching methods
lessons, seminar and home works.
Assessment methods
The final exam consists in areport on a project at the end of the course and it aims to assess the achievement of learning objectives:
- To know the methodologies of the discipline in particular on data analysis, on numerical simulations and on solution visualization.
- To understand the characteristics of the various physical and social systems to which the methodologies discussed can be applied.
Teaching tools
personal PC. videoprojector, internet
Office hours
See the website of Armando Bazzani