Power Laws are Logarithmic Boltzmann Laws

Details Power Laws are Logarithmic Boltzmann Laws Power Laws are Logarithmic Boltzmann Laws

1996-07-15

arxiv.org/abs/adap-org/9607001v1

Physics

Condensed Matter

latex, 9 pages with 3 figures

Scientific paper

10.1142/S0129183196000491

Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized elementary variables. In terms of the original variables this gives a power-law distribution. This mechanism implies certain relations between the constraints of the system, the power of the distribution and the dispersion law of the fluctuations. These predictions are validated by Monte Carlo simulations and experimental data. We speculate that stochastic multiplicative dynamics might be the natural origin for the emergence of criticality and scale hierarchies without fine-tuning.

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