Power laws are logarithmic Boltzmann laws

Moshe Levy*, Sorin Solomon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

210 Scopus citations


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.

Original languageAmerican English
Pages (from-to)595-601
Number of pages7
JournalInternational Journal of Modern Physics C
Issue number4
StatePublished - Aug 1996


  • Boltzmann Law
  • Lévy Distribution
  • Multiplicative Stochastic
  • Non-Equilibrium Complex Systems
  • Pareto
  • Power Laws
  • Self-Organization


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