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Natural distribution.

Tiia Grönholm1, Arto Annila

  • 1Department of Physical Sciences, Institute of Biotechnology, FI-00014, University of Helsinki, Finland.

Mathematical Biosciences
|September 8, 2007
PubMed
Summary
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Log-normal distributions, common in science, may arise from increasing entropy. This principle drives multiplicative variations, explaining skewed data patterns observed in nature.

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • General Science

Background:

  • Log-normal distributions are prevalent across various scientific disciplines.
  • The underlying mechanisms generating these skewed distributions remain largely unexplained.
  • Understanding their origin is crucial for interpreting diverse datasets.

Purpose of the Study:

  • To propose a fundamental basis for log-normal distributions.
  • To link the emergence of skewed distributions to the principle of increasing entropy.
  • To identify characteristic features of natural processes that yield such distributions.

Main Methods:

  • Conceptual framework linking entropy and multiplicative variations.
  • Analysis of thermodynamic states and chemical potentials.

Related Experiment Videos

  • Examination of cumulative curves of skewed distributions.

    • Main Results:

    • Log-normal distributions are hypothesized to result from the principle of increasing entropy.
    • Fluctuations during evolution towards probable states cause multiplicative variations.
    • Non-linear dispersion of thermodynamic states underlies the observed skewness.
    • Skewed distributions lacking integrable analytical forms are indicative of natural processes.

    Conclusions:

    • Increasing entropy provides a unifying explanation for log-normal distributions in nature.
    • Thermodynamic principles govern the multiplicative variations leading to skewed data.
    • The study offers a new perspective on the ubiquity of log-normal patterns in scientific data.