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
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

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:

Bashkirov AG, RAS, Inst Dynam Geospheres, Leninskii Prosp 38, Bldg 6, Moscow
117979, Russia.
RAS, Inst Dynam Geospheres, Moscow 117979, Russia.


IDS Number:


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


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