PHYSICS OF COMPLEX SYSTEMS
Course objectives
A - Knowledge and understanding OF 1) To possess a basic knowledge of complexity science, i.e. the collective properties that emerge with a large number of interacting components (atoms, particles or bacteria in a physical or biological context, or people, machines or businesses in a socio-economic context). OF 2) Understanding the mechanisms underlying the emergence of complex macroscopic properties from knowledge of microscopic mechanisms. OF 3) Mastering the basic toolbox of a complexity scientist: information theory, network theory, scale invariance and critical phenomena, properties of dynamical systems, agent models. B - Application skills OF 4) Knowing how to devise simple models for complex phenomenologies. OF 5) Being able to tackle complex problems analytically or computationally, translating research questions into concrete solution and verification actions. OF 6) Being able to apply the techniques and methods learnt also outside the areas covered in the course. OF 7) Integrating the knowledge acquired in order to formalise problems and obtain results and predictions of increasing accuracy. C - Autonomy of judgment OF 8) Being able to analyse phenomena, also through the acquisition of data and evidence, that fall within the scope of complexity and identify their essential elements. OF 9) Being able to synthesise phenomenologies in order to be able to distill relevant and relevant questions. OF 10) Being able to identify interesting new research directions. D - Communication skills OF 11) Being able to communicate complex issues in a simple way, focusing on the essential elements and revealing cause-effect relationships as far as possible. OF 12) Being able to organise a coherent, profound yet comprehensible presentation. OF 13) Knowing how to express one's thoughts in a way that stimulates group work and interaction with colleagues. E - Ability to learn OF 14) Have the ability to consult reference texts and articles. OF 15) Being able to assess the relevance of results, their place in the scientific panorama of reference and their potential importance for the research topics of interest. OF 16) Being able to design and develop a research project, identifying the main objectives and the possible paths to reach them.
Channel 1
VITTORIO LORETO
Lecturers' profile
Program - Frequency - Exams
Course program
Introduction to Complex Systems: Hierarchical structure of nature, reductionism and complexity. Complex and complicated. Introduction to the notion of entropy and complexity in Thermodynamics and Statistical Physics, Dynamic Systems Theory, Information Theory and Algorithmic Complexity Theory. Maximum entropy principle and maximum likelihood principle. Power laws: Power law distributions, properties and representations. Zipf's law, Heaps' law and its relation with Zipf's law. Taylor's law. Generative models. Critical self-organisation and fractal growth: physical models of self-organised fractal growth; Sandpile model and Forest Fire; Hints about mean-field theories and renormalization group approaches. Graphs and complex networks: Examples of complex networks in different areas; Historical perspective; Basics of graph theory; Generative models;. Dynamics on networks. Innovation dynamics: Motivation and definition; The Hoppe model. Discussion on the adjacent possible principle. Urn model with triggering and its applications. Seminars on specific research topics related to complex systems: Social dynamics (e.g. consensus dynamics in linguistics, dynamics of opinions, cultural evolution); Information dynamics (infosphere, recommendation systems, misinformation and echo chambers, etc.); Urban dynamics (from the microscopic level of mobility to the macroscopic level of modelling socio-economic interactions); Econophysics and Economic Complexity; Neural networks and Artificial Intelligence.
Prerequisites
a) It is essential to have a good grounding in statistical physics, calculus of probability and physics of dynamic systems.
b) Good analytical and computational knowledge is important.
c) Notions of data science and a strong inclination towards theoretical modelling are useful.
Books
The reference texts and teaching materials will be indicated by the teachers during the course and reported on the course web page.
Frequency
Attendance at all classes is strongly recommended.
Exam mode
The final examination will consist of an oral test in two consecutive stages. (i) the presentation of a
paper on an advanced topic chosen by the student and agreed with one of the lecturers. (ii) a series of open questions on the fundamental topics of the course. In the assessment of the examination, the determination of the final mark takes into account the following elements:
1. Competence in the core topics of the course: 60%.
2. Preparation and presentation of the thesis: 40%
In order to pass the examination, a mark of at least 18/30 is required.
In order to obtain a mark of 30/30 with distinction, the student must demonstrate that he/she has acquired an excellent knowledge of all the topics covered in the course, is able to link them in a logical and coherent manner and has shown initiative and ability in the preparation of the thesis. He/she also has to show independence of judgement, initiative and critical capacity in general.
Lesson mode
All details can be found on the course webpage:
https://sites.google.com/site/sistemicomplessisapienza/course-of-physics-of-complex-systems?authuser=0
VITTORIO LORETO
Lecturers' profile
Program - Frequency - Exams
Course program
Introduction to Complex Systems: Hierarchical structure of nature, reductionism and complexity. Complex and complicated. Introduction to the notion of entropy and complexity in Thermodynamics and Statistical Physics, Dynamic Systems Theory, Information Theory and Algorithmic Complexity Theory. Maximum entropy principle and maximum likelihood principle. Power laws: Power law distributions, properties and representations. Zipf's law, Heaps' law and its relation with Zipf's law. Taylor's law. Generative models. Critical self-organisation and fractal growth: physical models of self-organised fractal growth; Sandpile model and Forest Fire; Hints about mean-field theories and renormalization group approaches. Graphs and complex networks: Examples of complex networks in different areas; Historical perspective; Basics of graph theory; Generative models;. Dynamics on networks. Innovation dynamics: Motivation and definition; The Hoppe model. Discussion on the adjacent possible principle. Urn model with triggering and its applications. Seminars on specific research topics related to complex systems: Social dynamics (e.g. consensus dynamics in linguistics, dynamics of opinions, cultural evolution); Information dynamics (infosphere, recommendation systems, misinformation and echo chambers, etc.); Urban dynamics (from the microscopic level of mobility to the macroscopic level of modelling socio-economic interactions); Econophysics and Economic Complexity; Neural networks and Artificial Intelligence.
Prerequisites
a) It is essential to have a good grounding in statistical physics, calculus of probability and physics of dynamic systems.
b) Good analytical and computational knowledge is important.
c) Notions of data science and a strong inclination towards theoretical modelling are useful.
Books
The reference texts and teaching materials will be indicated by the teachers during the course and reported on the course web page.
Frequency
Attendance at all classes is strongly recommended.
Exam mode
The final examination will consist of an oral test in two consecutive stages. (i) the presentation of a
paper on an advanced topic chosen by the student and agreed with one of the lecturers. (ii) a series of open questions on the fundamental topics of the course. In the assessment of the examination, the determination of the final mark takes into account the following elements:
1. Competence in the core topics of the course: 60%.
2. Preparation and presentation of the thesis: 40%
In order to pass the examination, a mark of at least 18/30 is required.
In order to obtain a mark of 30/30 with distinction, the student must demonstrate that he/she has acquired an excellent knowledge of all the topics covered in the course, is able to link them in a logical and coherent manner and has shown initiative and ability in the preparation of the thesis. He/she also has to show independence of judgement, initiative and critical capacity in general.
Lesson mode
All details can be found on the course webpage:
https://sites.google.com/site/sistemicomplessisapienza/course-of-physics-of-complex-systems?authuser=0
FRANCESCA TRIA
Lecturers' profile
Program - Frequency - Exams
Course program
The course is divided into two main sections.
The first part of the course (about 36 hours) is devoted to the basic knowledge and tools of a complexity physicist. The main topics covered in this section are as follows. Introduction to Complex Systems: Hierarchical structure of nature, reductionism and complexity. Recall of the notion of entropy and complexity in Thermodynamics and Statistical Physics, Information Theory and Algorithmic Complexity Theory. Entropy in Dynamic Systems Theory. Recalls on Scaling laws and critical phenomena. Power law distributions and generative models. Critical self-organisation and fractal growth: physical models of self-organised fractal growth. Complex networks: topological properties of graphs, adjacency matrix, distributions, correlations. Poissonian networks and scale invariants. Clustering and communities. Growth models of complex networks. Notes on real complex networks.
The second part (for about 24 hours) is in-depth and will consist of a series of advanced seminars on a number of leading topics in complex systems science. Examples of topics covered include, but are not limited to: Social dynamics (e.g. consensus dynamics in linguistics, dynamics of opinions, cultural evolution); Innovation dynamics (models of increasing complexity and comparison with empirical data of systems showing innovation); Information dynamics (infosphere, recommendation systems, misinformation and echo chambers, etc.); Urban dynamics (from the microscopic level of mobility to the macroscopic level of modelling socio-economic interactions); Economic complexity.
Books
The reference texts and teaching materials will be indicated by the teachers during the course and reported on the course web page.
Frequency
It is not compulsory, but highly recommended.
Exam mode
The final examination will consist of an oral test in two consecutive stages. (i) the presentation of a
paper on an advanced topic chosen by the student and agreed with one of the lecturers. (ii) a series of open questions on the fundamental topics of the course. In the assessment of the examination, the determination of the final mark takes into account the following elements:
1. Competence in the core topics of the course: 60%.
2. Preparation and presentation of the thesis: 40%
In order to pass the examination, a mark of at least 18/30 is required.
In order to obtain a mark of 30/30 with distinction, the student must demonstrate that he/she has acquired an excellent knowledge of all the topics covered in the course, is able to link them in a logical and coherent manner and has shown initiative and ability in the preparation of the thesis. He/she also has to show independence of judgement, initiative and critical capacity in general.
FRANCESCA TRIA
Lecturers' profile
Program - Frequency - Exams
Course program
The course is divided into two main sections.
The first part of the course (about 36 hours) is devoted to the basic knowledge and tools of a complexity physicist. The main topics covered in this section are as follows. Introduction to Complex Systems: Hierarchical structure of nature, reductionism and complexity. Recall of the notion of entropy and complexity in Thermodynamics and Statistical Physics, Information Theory and Algorithmic Complexity Theory. Entropy in Dynamic Systems Theory. Recalls on Scaling laws and critical phenomena. Power law distributions and generative models. Critical self-organisation and fractal growth: physical models of self-organised fractal growth. Complex networks: topological properties of graphs, adjacency matrix, distributions, correlations. Poissonian networks and scale invariants. Clustering and communities. Growth models of complex networks. Notes on real complex networks.
The second part (for about 24 hours) is in-depth and will consist of a series of advanced seminars on a number of leading topics in complex systems science. Examples of topics covered include, but are not limited to: Social dynamics (e.g. consensus dynamics in linguistics, dynamics of opinions, cultural evolution); Innovation dynamics (models of increasing complexity and comparison with empirical data of systems showing innovation); Information dynamics (infosphere, recommendation systems, misinformation and echo chambers, etc.); Urban dynamics (from the microscopic level of mobility to the macroscopic level of modelling socio-economic interactions); Economic complexity.
Books
The reference texts and teaching materials will be indicated by the teachers during the course and reported on the course web page.
Frequency
It is not compulsory, but highly recommended.
Exam mode
The final examination will consist of an oral test in two consecutive stages. (i) the presentation of a
paper on an advanced topic chosen by the student and agreed with one of the lecturers. (ii) a series of open questions on the fundamental topics of the course. In the assessment of the examination, the determination of the final mark takes into account the following elements:
1. Competence in the core topics of the course: 60%.
2. Preparation and presentation of the thesis: 40%
In order to pass the examination, a mark of at least 18/30 is required.
In order to obtain a mark of 30/30 with distinction, the student must demonstrate that he/she has acquired an excellent knowledge of all the topics covered in the course, is able to link them in a logical and coherent manner and has shown initiative and ability in the preparation of the thesis. He/she also has to show independence of judgement, initiative and critical capacity in general.
- Lesson code10592568
- Academic year2025/2026
- CoursePhysics
- CurriculumCondensed matter physics: Theory and experiment (Percorso valido anche fini del conseguimento del titolo multiplo italo-francese-portoghese-canadese) - in lingua inglese
- Year2nd year
- Semester1st semester
- SSDFIS/03
- CFU6