Entropy and irreversibility in dynamical systems

Oliver Penrose*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


A method of defining non-equilibrium entropy for a chaotic dynamical system is proposed which, unlike the usual method based on Boltzmann's principle S = k log W, does not involve the concept of a macroscopic state. The idea is illustrated using an example based on Arnold's 'cat' map. The example also demonstrates that it is possible to have irreversible behaviour, involving a large increase of entropy, in a chaotic system with only two degrees of freedom.

Original languageEnglish
Article number20120349
Number of pages11
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2005
Publication statusPublished - 28 Dec 2013


  • irreversibility
  • entropy
  • Boltzmann's principle
  • Arnold map
  • macrostates
  • chaotic dynamical system


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