Pier Luigi Gentili is Ph.D. in Chemistry. His research and teaching activities are focused on Complex Systems. He is trusting in Natural Computing as an effective strategy to understand Complex Systems and face the Computational Complexity Challenges. In particular, he is developing the innovative Chemical Artificial Intelligence. He has several collaborations and work experience in many laboratories. For instance, the "Photochemistry and Photophysics Group" of the University of Perugia (Italy); the "Nonlinear Dynamics Group" of the Brandeis University (USA); the "European Laboratory of Nonlinear Spectroscopy" in Florence (Italy); the "Center for Photochemical Sciences" of the Bowling Green State University (USA); the "Laboratory of Computational Chemistry and Photochemistry" of University of Siena (Italy).

ORCID: 0000-[...].

Introduction.

Reversibility or Irreversibility? That is the Question!

Out-of-Equilibrium Thermodynamics.

An amazing scientific voyage: from equilibrium up to self-organization through bifurcations.

The emergence of temporal order in ecosystems.

The emergence of temporal order in economy.

The emergence of temporal order within a living being.

The emergence of temporal order in a chemical laboratory.

The emergence of order in space.

The emergence of chaos in time.

Chaos in space: The Fractals.

Complex Systems

How to untangle Complex Systems?

Appendix A: Numerical Solutions of Differential Equations

Appendix B: The Maximum Entropy Method

Appendix C: Fourier Transform of Waveforms

Appendix D: Errors and Uncertainties in Laboratory Experiments

Appendix E: Errors in Numerical Computation