Natural selection for least action

Ville R.I. Kaila, Arto Annila

Research output: Contribution to journalArticlepeer-review

99 Scopus citations


The second law of thermodynamics is a powerful imperative that has acquired several expressions during the past centuries. Connections between two of its most prominent forms, i.e. the evolutionary principle by natural selection and the principle of least action, are examined. Although no fundamentally new findings are provided, it is illuminating to see how the two principles rationalizing natural motions reconcile to one law. The second law, when written as a differential equation of motion, describes evolution along the steepest descents in energy and, when it is given in its integral form, the motion is pictured to take place along the shortest paths in energy. In general, evolution is a non-Euclidian energy density landscape in flattening motion.

Original languageEnglish
Pages (from-to)3055-3070
Number of pages16
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2099
StatePublished - 8 Nov 2008
Externally publishedYes


  • Coordinate
  • Energy transfer
  • Entropy
  • Evolution
  • Metric
  • Natural process


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