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Power Laws Are Logarithmic Boltzmann Laws

Author

Listed:
  • MOSHE LEVY

    (Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel)

  • SORIN SOLOMON

    (Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel)

Abstract

Multiplicative random processes in (not necessarily 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 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.

Suggested Citation

  • Moshe Levy & Sorin Solomon, 1996. "Power Laws Are Logarithmic Boltzmann Laws," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 595-601.
    • Handle: RePEc:wsi:ijmpcx:v:07:y:1996:i:04:n:s0129183196000491
    DOI: 10.1142/S0129183196000491
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