- Docente: Armando Bazzani
- Credits: 6
- SSD: MATH-04/A
- Language: Italian
- Teaching Mode: In-person learning (entirely or partially)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Physics (cod. 9244)
-
from Sep 21, 2026 to Dec 22, 2026
Learning outcomes
Basic knowledge of physical and mathematical methods to develop dynamic and statistical model for the study of complex systems.
Course contents
The primary objective of the "Introduction to the Physics of Complex Systems" course is to show how mathematical physics has addressed the issue of complexity in biological, social, and economic systems. In particular, the concept of the physical model will be explored in depth through the results of dynamical systems theory.
The construction of a model for a complex system will be discussed in order to understand the role of the interaction structure among elementary components through the use of complex networks.
The concept of a stochastic differential equation will be introduced via the Central Limit Theorem, alongside that of a stochastic dynamical system; topics will include the properties of Markov processes on discrete spaces, the concepts of entropy and entropy production, equilibria satisfying detailed balance and stochastic reversibility, and Maximum Entropy principles.
The course will present the following topics using models from the physics of complex systems, including examples of models with applications to physical chemistry, biology, economics, and social systems.
Study of empirical distributions obtained from big data for complex systems: exponential laws and power laws.
Analytical and numerical methods for the analysis and validation of a deterministic and stochastic dynamical system.
Introduction to the concept of a network for representing interaction structures, and definition of a dynamical system on a graph.
Introduction to Statistical Mechanics, the concept of emergent properties, critical states, and phase transitions.
Concept of emergent property: phase transitions, synchronization, formation of solitary waves.
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