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.
|Number of pages||11|
|Journal||Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - 28 Dec 2013|
- Boltzmann's principle
- Arnold map
- chaotic dynamical system