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Details for:
Schulman L. When Things Grow Many. Complexity,...in Nature 2021
schulman l when things grow many complexity nature 2021
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E-books
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1
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9.6 MB
Uploaded On:
Feb. 17, 2022, 10:22 a.m.
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andryold1
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Textbook in PDF format Aimed at advanced undergraduates and graduate students, When Things Grow Many is an accessible and engaging textbook introducing the theory of statistical mechanics, as well as its fascinating real-world applications. The book's original approach, which covers interdisciplinary applications of statistical mechanics to a wide range of subjects, including chemistry, biology, linguistics, economics, sociology and more, is bound to appeal to a wide audience. While the first part of the book introduces the various methods of statistical physics, including complexity, emergence, universality, self-organized criticality, power laws and other timely topics, the final sections focus on specific relevance of these methods to the social, biological and physical sciences. The mathematical content is woven throughout the book in the form of equations, as well as further background and explanations being provided in footnotes and appendices. Introduction Building Ideal gas Fluctuations of the ideal gas Rubber bands The game Analysis Simulation Independent folk What actually happens How often does the prediction go wrong? Percolitis An epidemic model Discussion Behavior of the order parameter near the critical point Approach to equilibrium Discreteness and fluctuations* Self-organized criticality (SOC): Applications to galaxies and mean field theory SOC in galaxies SOC in a mean field theory The truth about percolitis Abstract percolation Percolation applications True epidemiology Ferromagnetism Curie–Weiss ferromagnets Magnetization Fluctuations greater than N Maximum entropy methods Information Maximum entropy Mathematical details* Constructing the probabilities* Using the probabilities Using maximum entropy to study Supreme Court voting Power laws Power laws are scale free Diffusion Preferential attachment (the rich get richer) Exponential functions of exponential distributions Superposition of exponentials Critical phenomena and self-organized criticality (SOC) Universality, renormalization and critical phenomena The nearest neighbor one-dimensional Ising model Mean field treatment Transfer matrix treatment* Spatial correlations* Renormalization group treatment Social sciences Econophysics Stock market bubbles and crashes Linguistics Zipf's law Power laws for cities Urban discrimination Voter models and elections Crowd control Traffic Cellular automaton models of traffic Biological sciences Firefly synchronization Other models for synchronization Biorobotics and glass Gene distributions Flocking Kuramoto model Ecology Neurology Physical sciences Power laws for luminescence Large scale structure Galactic morphology Putting it all together Appendix A Notation Appendix B Background in statistical physics Appendix C Fractals Appendix D Review of probability Basics Counting The central limit theorem Markov processes Stochastic dynamics The notion of probability Stirling's approximation Exercises in probability Appendix E The van der Waals gas Appendix F The logistic map Appendix G Lagrange multipliers Two variables, one constraint Generalization, more than one constraint Example Appendix H Complexity in the observable representation The observable representation Appendix I A Quotation Appendix J Solutions to exercises References Index
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Schulman L. When Things Grow Many. Complexity,...in Nature 2021.pdf
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