Untangling Complex Systems A Grand Challenge for Science

Complex Systems are natural systems that science is unable to describe exhaustively. Examples of Complex Systems are both unicellular and multicellular living beings; human brains; human immune systems; ecosystems; human societies; the global economy; the climate and geology of our planet. This book is an account of a marvelous interdisciplinary journey the author made to understand properties of the Complex Systems. He has undertaken his trip, equipped with the fundamental principles of physical chemistry, in particular, the Second Law of Thermodynamics that describes the spontaneous evolution of our universe, and the tools of Non-linear dynamics. By dealing with many disciplines, in particular, chemistry, biology, physics, economy, and philosophy, the author demonstrates that Complex Systems are intertwined networks, working in out-of-equilibrium conditions, which exhibit emergent properties, such as self-organization phenomena and chaotic behaviors in time and space.

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

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: 0000-0003-1092-9190.