title: Entropy and irreversibility in dynamical systems.
abstract: 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 = klog 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.
authors.affiliation: Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Colin Maclaurin Building, Heriot-Watt University, , Riccarton, Edinburgh EH14 4AS, UK.
authors.forename: Oliver
authors.initials: O
authors.lastname: Penrose
keywords: Arnold map; Boltzmann’s principle; chaotic dynamical system; entropy; irreversibility; macrostates