ABS: Bashkirov Information entropy and power-law distributions for chaotic systems
Gretchen Whitney
gwhitney at UTKUX.UTCC.UTK.EDU
Tue Nov 28 18:11:55 EST 2000
Bashkirov AG : e-mail : abas at orig.ipg.msk.su
TITLE Information entropy and power-law distributions for chaotic
systems
AUTHOR Bashkirov AG, Vityazev AV
JOURNAL PHYSICA A 277: (1-2) 136-145 MAR 1 2000
Document type: Article Language: English Cited References: 27
Times Cited: 0
Abstract:
The power law is found for density distributions for the chaotic systems of
most different nature (physical, geophysical, biological,
economical, social, etc.) on the basis of the maximum entropy principle for
the Renyi entropy. Its exponent q is expressed as a
function q(beta) of the Renyi parameter beta. The difference between the
Renyi and Boltzmann-Shannon entropies (a modified
Lyapunov functional Lambda(R)) for the same power-law distribution is
negative and as a function of beta has a well-defined
minimum at beta* which remains within the narrow range from 1.5 to 3 when
varying other characteristic parameters of any concrete
systems. Relevant variations of the exponent q(beta*) are found within the
range 1-3.5. The same range of observable values of q is
typical for the various applications where the power-law distribution takes
glace. It is known under the following names: "triangular
or trapezoidal" (in physics and technics), "Gutenberg-Richter law" (in
geophysics), "Zipf-Pareto law" (in economies and the
humanities), "Lotka low" (in science of science), etc. As the negative
Lambda(R) indicates self-organisation of the system, the
negative minimum of Lambda(R) corresponds to the most self-organised state.
Thus, the comparison between the calculated range
of variations of q(beta*) and observable values of the exponent q testifies
that the most self-organised states are as a rule realised
regardless of the nature of a chaotic system. (C) 2000 Elsevier Science B.V.
All rights reserved.
Author Keywords:
maximum entropy principle, power-law distribution, Renyi entropy
KeyWords Plus:
STATISTICAL-MECHANICS, SELF-ORGANIZATION
Addresses:
Bashkirov AG, RAS, Inst Dynam Geospheres, Leninskii Prosp 38, Bldg 6, Moscow
117979, Russia.
RAS, Inst Dynam Geospheres, Moscow 117979, Russia.
Publisher:
ELSEVIER SCIENCE BV, AMSTERDAM
IDS Number:
292VJ
ISSN:
0378-4371
Cited Author Cited Work Volume Page Year
BASHKIROV AG NONEQUILIBRIUM STAT 1995
BASHKIROV AG PLANET SPACE SCI 44 909 1996
BECK C THERMODYNAMICS CHAOT 1993
BINZEL RP ASTEROIDS 2 1989
CHAME A J PHYS A-MATH GEN 27 3663 1994
CHAME A PHYSICA A 255 423 1998
HAKEN H INFORMATION SELF ORG 1988
JAYNES ET BRANDIES LECT 3 160 1963
JAYNES ET PHYS REV 106 620 1957
KASAHARA K EARTHQUAKE MECH 1981
KATZ A PRINCIPLES STAT MECH 1967
KHINCHIN AY MATH FDN INFORMATION 1957
KLIMONTOVICH YL CHAOS SOLITON FRACT 5 1985 1995
KLIMONTOVICH YL PHYSICA A 142 390 1987
KLIMONTOVICH YL STAT THEORY OPEN SYS 1994
LOSEE RM SCI INFORMATION 1990
MANDELBROT B J POLIT ECON 71 421 1963
PLASTINO AR PHYSICA A 222 347 1995
PRICE D LITTLE SCI BIG SCI 1963
RAMSHAW JD PHYS LETT A 175 171 1993
RENYI A PROBABILITY THEORY 1970
SHORE JE IEEE T INFORM THEORY 26 26 1980
SHRODINGER E STAT THERMODYNAMICS 1946
TSALLIS C J STAT PHYS 52 479 1988
VITYAZEV AV TERRESTIAL PLANETS O 1990
ZAKHAROV VE SOV PHYS JETP-USSR 24 455 1967
ZUBAREV DN NONEQUILIBRIUM STAT 1974
WHEN RESPONDING PLEASE ATTACH THIS MESSAGE
-------------------------------------------------------------
(c) ISI, Reprinted with permission
Please visit their website at www.isinet.com
-------------------------------------------------------------
More information about the SIGMETRICS
mailing list