Kac’s ring: Entropy and Poincaré recurrence

Aravind Chandrasekaran and Sudhir R. Jain

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 14, 3702-3707

Abstract: We study the entropy of an N-site Kac ring in a non-equilibrium state. As the system dynamically evolves towards equilibrium and eventually to the initial state exhibiting Poincaré recurrence, we see that the entropy saturates over a period of time which is large for large N. At about the time of order N, the system starts to return to its initial state. We show that there is indeed a perfect “recurrence of statistical fluctuations”, which we are able to explore, as Kac’s ring possesses a finite recurrence time. Entropy is shown here to be a periodic function of the Poincaré recurrence time.

Keywords: Boltzmann H-function; Von Neumann entropy; Poincaré recurrence; Irreversibility (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:14:p:3702-3707

DOI: 10.1016/j.physa.2012.02.010

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