Since the inception of the Mathematical Theory of Communication by Claude Shannon in 1938, a vast theory has unfolded to formulate and optimise the quantification of information and its transfer across communication systems. Applications have since ranged from signal processing and information flow over computer networks to eliciting predictive ability across complex natural systems. Information Theory became a scientific field in its own right, having later ventured onto broader paradigms boosted by quantum mechanics and nonlinear dynamics developments.

Underneath the statistical principles of Information Theory lie fundamental Physics. The information laws are not arbitrary, but rather the reflex of core principles in Thermodynamics and Statistical Physics. These stem back to earlier foundations from such diverse contributors as Boltzmann, Fermi, Fokker, Planck and Einstein, along with kinematic geometric advances from Kolmogorov, Sinai, Pesin, Ruelle and Young.

In Information Physics, the concept of information and its characterisation are formulated from an underlying unified theoretical physics. This brings a deeper understanding about why information is the way it is and behaves the way it does, placing statistical attributes into a first principle physical background aiming at universality. It further provides more robust methodologies for information quantification, storage, transmission and optimisation, opening new avenues laid down by the very same physics that governs information dynamics in the first place.

The course starts with an overview on Information Theory, classical and quantum, then progressing to dynamical system theories and kinematic geometry. The last sector entails the theoretical physics of information and complexity being developed by the course coordinator, including his recently introduced non-ergodic theory of information physics and synergistic dynamic theory of complex coevolutionary systems, along with applications spanning from signal processing, machine learning, telecommunications, network design and optimisation in structurally evolving complex systems.

This course is also delivered as **Information Physics, Nonlinear Dynamics and Complexity**, with the following schematic structure:

A – Theory: Physics fundamentals behind the nature, geometry and nonlinear dynamics of information and emergence of complexity;

B – Tools: Methods and algorithms from the mathematical physics of information for complex data analytics and model design. From nonlinear dynamic and statistical IT to broader computational information physics tools for data mining, machine learning, adaptive computing and Artificial Intelligence design.

C – GeoSys Operation: Operational real-world examples for a) data mining and machine learning in large satellite datasets; b) nonlinear analytics and model design for earth system dynamics; c) early warning and automated decision support systems in hydro-meteorological hazards;

D – Frontier Operation: a) from nonlinear classical to quantum machine learning and cryptography; b) early warning detection and adaptive decision support of critical transitions in nonlinear climate dynamics, econometrics, insurance and defense.

E – Hands-On: Simple analytical and computational exercises on the prior points.

Since 2017, recent geophysically-oriented variants have been deployed for:

Physics target audience: **Information Physics from Quantum Gravitation to Thermodynamic Cosmology.**

Geoinformation target audience: **Information Physics: Theoretical Advances and Geophysical Applications**.

Cite as:

Perdigão, R.A.P. (2017): *Course on Information Physics and Evolutionary Complexity.* https://doi.org/10.46337/uc.170910.

Enquiries are welcome for registering at our regular courses at M-DSC or requesting course deployment at external institutions.