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This book presents the concepts needed to deal with self-organizing complex systems from a unifying point of view that uses macroscopic data. The various meanings of the concept "information" are discussed and a general formulation of the maximum information (entropy) principle is used. With the aid of results from synergetics, adequate objective constraints for a large class of self-organizing systems are formulated and examples are given from physics, life and computer science. The relationship to chaos theory is examined and it is further shown that, based on possibly scarce and noisy data, unbiased guesses about processes of complex systems can be made and the underlying deterministic and random forces determined. This allows for probabilistic predictions of processes, with applications to numerous fields in science, technology, medicine and economics. The extensions of the third edition are essentially devoted to an introduction to the meaning of information in the quantum context. Indeed, quantum information science and technology is presently one of the most active fields of research at the interface of physics, technology and information sciences and has already established itself as one of the major future technologies for processing and communicating information on any scale. This book addresses graduate students and nonspecialist researchers wishing to get acquainted with the concept of information from a scientific perspective in more depth. It is suitable as a textbook for advanced courses or for self-study.

Self-organizing systems. --- Entropy (Information theory) --- Ergodic theory --- Information theory --- Learning systems (Automatic control) --- Self-optimizing systems --- Cybernetics --- Intellect --- Learning ability --- Synergetics --- System theory. --- Neurosciences. --- Data structures (Computer scienc. --- Complex Systems. --- Systems Theory, Control. --- Condensed Matter Physics. --- Biological and Medical Physics, Biophysics. --- Data Structures and Information Theory. --- Data structures (Computer science) --- Neural sciences --- Neurological sciences --- Neuroscience --- Medical sciences --- Nervous system --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Systems theory. --- Statistical physics. --- Dynamical systems. --- Condensed matter. --- Biophysics. --- Biological physics. --- Data structures (Computer science). --- Biological physics --- Biology --- Physics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Mathematical statistics --- Statistical methods

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This volume of the “Encyclopedia of Complexity and Systems Science, Second Edition” (ECSS), introduces the fundamental physical and mathematical concepts underlying the theory of complex physical, chemical, and biological systems. Numerous applications illustrate how these concepts explain observed phenomena in our daily lives, which range from spatio-temporal patterns in fluids from atmospheric turbulence in hurricanes and tornadoes to feedback dynamics of laser intensity to structures in cities and rhythms in the brain. The spontaneous formation of well-organized structures out of microscopic system components and their interactions is one of the most fascinating and challenging phenomena for scientists to understand. Biological systems may also exhibit organized structures emanating from interactions of cells and their networks. For instance, underlying structures in the brain emerge as certain mental states, the ability to coordinate movement, or pathologies such as tremor or epileptic seizures. When we try to explain or understand these extremely complex biological phenomena, it is natural to ask whether analogous processes of self-organization may be found in much simpler systems of the inanimate world. In recent decades, it has become increasingly evident that there exist numerous examples in physical and chemical systems in which well-organized spatio-temporal structures arise out of disordered states. As in living organisms, the functioning of these systems can be maintained only by a flux of energy (and matter) through them. Synergetics combines elements from physics and mathematics to explain how a diversity of systems obey the same basic principles. All chapters in this volume have been thoroughly revised and updated from the first edition of ECSS. The second edition also includes new or expanded coverage of such topics as chaotic dynamics in laser systems and neurons, novel insights into the relation of classical chaos and quantum dynamics, and how noise in the brain tunes observed neural activity and controls animal and human behavior. .

Statistical physics. --- Neural networks (Computer science) . --- Computational complexity. --- Systems biology. --- System theory. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Mathematical Models of Cognitive Processes and Neural Networks. --- Complexity. --- Systems Biology. --- Statistical Physics and Dynamical Systems. --- Complex Systems. --- Systems, Theory of --- Systems science --- Science --- Computational biology --- Bioinformatics --- Biological systems --- Molecular biology --- Complexity, Computational --- Electronic data processing --- Machine theory --- Artificial neural networks --- Nets, Neural (Computer science) --- Networks, Neural (Computer science) --- Neural nets (Computer science) --- Artificial intelligence --- Natural computation --- Soft computing --- Physics --- Mathematical statistics --- Philosophy --- Statistical methods --- Synergetics. --- Applied mathematics. --- Chaotic behavior in systems. --- Mathematical modelling. --- Mathematical physics. --- Maths for engineers. --- Neural networks (Computer science) --- Optical physics. --- Science. --- Research. --- Self-organizing systems.