Nonextensive Entropy: Interdisciplinary Applications (Santa Fe Institute Studies on the Sciences of Complexity) 1st Edition by Murray Gell-Mann (PDF)

Description

A great variety of complex phenomena in many scientific fields exhibit power-law behavior, reflecting a hierarchical or fractal structure. Many of these phenomena seem to be susceptible to description using approaches drawn from thermodynamics or statistical mechanics, particularly approaches involving the maximization of entropy and of Boltzmann-Gibbs statistical mechanics and standard laws in a natural way. The book addresses the interdisciplinary applications of these ideas, and also on various phenomena that could possibly be quantitatively describable in terms of these ideas.

User’s Reviews

Editorial Reviews: Review “Gell-Mann (Science Board, Santa Fe Institute) and Tsallis (Brazilian Center for Physics Research) present material on interdisciplinary applications of ideas related to the nonextensive generalization of entropy, Boltzmann- Gibbs statistical mechanics, and standard thermodynamics. Applications relate to dynamical, physical, geophysical, biological, economic, financial, and social systems, and to networks, linguistics, and plectics. A dripping faucet as a nonextensive system, the pricing of stock options, and spatial patterns in forest ecology are some subjects discussed. Material originated at an April 2002 workshop held at the Santa Fe Institute.”–SciTech Book News About the Author Murray Gell-Mann is a Professor at Sante Fe Institute. Tsallis Constantino is at the Brazilian Center for Physics Research.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book is nice. However, the topic is a bit controversial.I work with classical entropy, but it’s nice to see what’s going onon the other end.

⭐.. about a student-t like distribution. Too much ado. There is no generalization of entropy (see the comment by Nauenberg and Balian in 2005 Europhysics News, e.g.) and no ‘generalized thermostatistics. In fact, there is nothing but a postulated distribution that (as do student-ts typically) has a Gaussian limit. So what?The claim of ‘nonlinear Fokker-Planck” and “nonlinear Markov processes” was quite easy to explode: There is no such thing as a ‘nonlinear Markov process’. There is no such thing as a ‘nonlinear Fokker-Planck equation’ for a conditional probability. A conditional probability with initial state memory is nonMarkovian. A conditional probability with initial state memory is not guaranteed to obey a Chapman-Kolmogorov equation and usually doesn’t. A Chapman-Kolmogorov equation is a necessary but not sufficient condition for a Markov process. A Fokker-Planck equation with memory of an initial state in its drift and/or diffusion coefficients does not generate a Markov process. A nonlinear diffusion equation does not define any stochastic process at all, in fact a diffusion equation for a 1-point density defines no stochastic process at all. A 1-point density cannot be used to identify/define a stochastic process, both scaling Markov processes and strongly nonMarkov processes like fractional Brownian motion have exactly the same 1-point density, with widely differing conditional densities. For detailed explanations see cond-mat/0701589 and references therein.It would be of interest to psychologists and sociologists to study and analyze how such ‘movements’, based on claims hanging in thin air, gain a multitude of followers and hangers-on, as this movement has. The literature over the last 10 years is riddled with wrong and empty papers on such stuff.

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