TY - JOUR

T1 - A short account of a connection of power laws to the information entropy

AU - Dover, Yaniv

PY - 2004/3/15

Y1 - 2004/3/15

N2 - We use the formalism of "maximum principle of Shannon's entropy" to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean "internal order" (Boltzmann entropy) of a complex, self-interacting, self-organized system. Since the Shannon entropy is equivalent to the Boltzmann's entropy under equilibrium, non-interacting conditions, we interpret this result as the complex system making use of its intra-interactions and its non-equilibrium in order to keep the equilibrium Boltzmann's entropy constant on the average, thus enabling it an advantage at surviving over less ordered systems, i.e., hinting towards an "Evolution of Structure". We then demonstrate the formalism using a toy model to explain the power laws observed in Cities' populations and show how Zipf's law comes out as a natural special point of the model. We also suggest further directions of theory.

AB - We use the formalism of "maximum principle of Shannon's entropy" to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean "internal order" (Boltzmann entropy) of a complex, self-interacting, self-organized system. Since the Shannon entropy is equivalent to the Boltzmann's entropy under equilibrium, non-interacting conditions, we interpret this result as the complex system making use of its intra-interactions and its non-equilibrium in order to keep the equilibrium Boltzmann's entropy constant on the average, thus enabling it an advantage at surviving over less ordered systems, i.e., hinting towards an "Evolution of Structure". We then demonstrate the formalism using a toy model to explain the power laws observed in Cities' populations and show how Zipf's law comes out as a natural special point of the model. We also suggest further directions of theory.

KW - Dynamical systems

KW - Information theory

KW - Power laws

KW - Self-organizing systems

KW - Statistical physics

UR - http://www.scopus.com/inward/record.url?scp=0742302967&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2003.09.029

DO - 10.1016/j.physa.2003.09.029

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AN - SCOPUS:0742302967

SN - 0378-4371

VL - 334

SP - 591

EP - 599

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 3-4

ER -