Physics of Fractal Operators (Paperback, Softcover reprint of the original 1st ed. 2003)

In Chapter One we review the foundations of statistieal physies and frac tal functions. Our purpose is to demonstrate the limitations of Hamilton's equations of motion for providing a dynamical basis for the statistics of complex phenomena. The fractal functions are intended as possible models of certain complex phenomena; physical.systems that have long-time mem ory and/or long-range spatial interactions. Since fractal functions are non differentiable, those phenomena described by such functions do not have dif ferential equations of motion, but may have fractional-differential equations of motion. We argue that the traditional justification of statistieal mechan ics relies on aseparation between microscopic and macroscopie time scales. When this separation exists traditional statistieal physics results. When the microscopic time scales diverge and overlap with the macroscopie time scales, classieal statistieal mechanics is not applicable to the phenomenon described. In fact, it is shown that rather than the stochastic differential equations of Langevin describing such things as Brownian motion, we ob tain fractional differential equations driven by stochastic processes."

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Institute for Nonlinear Science
Release date:	May 2011
First published:	2003
Authors:	Bruce West • Mauro Bologna • Paolo Grigolini
Dimensions:	235 x 155 x 19mm (L x W x T)
Format:	Paperback
Pages:	354
Edition:	Softcover reprint of the original 1st ed. 2003
ISBN-13:	978-1-4419-3054-5
Categories:	Books > Science & Mathematics > Mathematics > Applied mathematics > Non-linear science Books > Science & Mathematics > Physics > Thermodynamics & statistical physics > Statistical physics Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics) > General
LSN:	1-4419-3054-X
Barcode:	9781441930545

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