Physics of complex phenomena

Common core courses  in statistical physics from Centrale Méditerranée.

The aim of this course is to acquire the knowledge and skills essential for analyzing complex phenomena in physics and complex systems in the engineering sciences. While emphasizing the general nature of the concepts covered, this course presents a wide range of application areas, with particular attention to the fundamental definitions of randomness, information and complexity. This course provides an introduction to a topical scientific field (Nobel Prize in Physics in 2021, 2022, 2024, Fields Medal in 2022, Abel Prize in 2024), and enables students to question the profound nature of physics while providing operational tools for engineers.

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Elements of information theory useful for physics and engineering (complexity, entropy and applications).

Complex scalar and vector phenomena and applications to waves and signals.

Quantum physical systems (density matrix, Von Neumann entropy and applications).

Disordered physical systems (random mathematics, frozen disorders, characterization techniques).

Introduction to chaotic phenomena.

Know how to define and characterize complexity in physics and engineering sciences,

master elementary techniques for analyzing certain complex systems or phenomena,

Apply fundamental concepts of information theory,

Understand the essential factors involved in the analysis of complex systems,

Acquire critical expertise in the interpretation of physical results.

2 supervised assignments, each contributing 50% of the final grade.

Ph. Réfrégier, « Noise Theory and Application to Physics » - Springer 2003.

T.M. Cover and J.A. Thomas, « Elements of Information Theory» - Wiley 2006.

C. Cohen-Tannoudji, F. Laloë and B. Diu, « Mécanique Quantique T.1 et 2 » - Edp Sciences (2018).

K. H. Fischer andJ. A. Hertz, « Spin Glasses» - Cambridge University Press 1991.

D. L. Stein and C. M. Newman, « Spin Glasses and Complexity» - Princeton University Press 2013.

Julien Fade

Philippe Réfrégier