Admission Requirements
Knowledge of the Equilibrium Thermodynamics.

Learning Outcomes
The graduate students in Chemical Science learn the principles of the Out-of-Equilibrium Thermodynamics and Non-Linear Dynamics only in “Investigation into Complex Systems”. This course's primary purpose is to give the students the conceptual and methodological bases to face the interdisciplinary analysis of Complex Systems.
The central notions that must be learned by students are:
•evolutive criteria of the physical and chemical systems in out-of-equilibrium conditions;
•self-organization;
•deterministic chaos and fractal structures;
•Natural and Computational Complexity.

All these notions will allow students to:
•predict the evolution of out-of-equilibrium systems;
•experimental investigation of the self-organizing chemical and physical systems;
•appreciate the limits of science in predicting the behavior of deterministic chaotic systems;
• characterize Fractal structures.

Programme
This course is included in the curriculum of the Master Degree in Chemical Sciences, which lasts two years.
The subjects proposed are:
1) Introduction to the Natural Complexity and the Science of Complexity.
2) Deepened analysis of the II Law of Thermodynamics.
3) Non-equilibrium Thermodynamics. Flows and Forces. Linear and Non-Linear regimes. Entropy Production and evolution criteria for the out-of-equilibrium systems.
4) Linear analysis of the stability of the stationary states: stable, unstable, and oscillatory stationary states.
5) Oscillatory chemical reactions, chemical waves, Turing structures, and periodic precipitations.
6) More insight on the Non-Linear regime: Bifurcations and deterministic Chaos. The case of convection.
7) Fractals.
8) Natural and Computational Complexities. Strategies to face Complexity Challenges.
Four experiments involving out-of-equilibrium systems are carried out in the laboratory.

References
The textbook used for this course is P. L. Gentili, “Untangling Complex Systems: A Grand Challenge for Science”, CRC Press, 2018, ISBN 9781466509429.

Teaching Methodology
The course is organized in two stages. The first stage consists of the frontal lessons proposed in the classroom and regarding all the course subjects. It is assisted by short movies extracted from the web.
The second stage consists of four experiments requiring six hours each. The experiments are carried out in the Photo-physics and Photochemistry Laboratory of the Chemistry, Biology and Biotechnology Department. Students are split into groups (having no more than three members) and perform the experiments in parallel by using separate facilities available in the laboratory.

Language of the Curriculum and Course
The course will be offered in English from the 2022/2023 Academic Year.

ECTS Credits
The Master Degree in Chemical Sciences lasts two years and includes 120 ECTS. The course “Investigation into Complex Systems” is offered in the second semester of the first year and is destined for all students who choose the Physical Chemistry curriculum

Examination Methodology
The acquisition of the course topics is tested in two ways:
1) the reports of the laboratory experiences.
2) An oral exam with questions about the subjects presented during the lectures.
The Professor must receive the students’ reports of the laboratory experiments before taking the oral test.

Relevance
This course is fundamental for developing the Joint Curriculum in Complex Systems Thinking for Sustainable Development. It offers the necessary knowledge for distinguishing the ontology and epistemology of Complex Systems. Furthermore, it gives the skills and competencies for facing the description of any Complex System.