Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2003-09-16
Physica A Vol. 334 (2004), issue: 3-4, pp. 591-599
Physics
Condensed Matter
Statistical Mechanics
7 pages, no figures, accepted for publication in "Physica A"
Scientific paper
10.1016/j.physa.2003.09.029
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.
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