Kac鈥檚 ring: Entropy and Poincar茅 recurrence

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• 作者：Aravind Chandrasekaran^a ; Sudhir R. Jain^b ; ^{srjain@barc.gov.in}
• 关键词：Boltzmann H-function ; Von Neumann entropy ; Poincaré ; recurrence ; Irreversibility
• 刊名：Physica A
• 出版年：2012
• 期刊代码：138_03784371
• 类别：et
• 出版时间：15 July, 2012
• 卷：391
• 期：14
• 页码：3702-3707
• 文件大小：516 K

摘要

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