Cohen Doron, Imry Yoseph
Department of Physics, Ben Gurion University of the Negev, Beer Sheva 84105, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 1):011111. doi: 10.1103/PhysRevE.86.011111. Epub 2012 Jul 9.
We obtain the Crooks and the Jarzynski nonequilibrium fluctuation relations using a direct quantum-mechanical approach for a finite system that is either isolated or coupled not too strongly to a heat bath. These results were hitherto derived mostly in the classical limit. The two main ingredients in the picture are the time-reversal symmetry and the application of the first law to the case where an agent performs work on the system. No further assumptions regarding stochastic or Markovian behavior are necessary, neither a master equation or a classical phase-space picture are required. The simplicity and the generality of these nonequilibrium relations are demonstrated, giving very simple insights into the physics.
我们采用直接量子力学方法，针对一个孤立的或与热浴耦合不太强的有限系统，得到了克鲁克斯（Crooks）和雅津斯基（Jarzynski）非平衡涨落关系。这些结果迄今为止大多是在经典极限下推导出来的。该图景中的两个主要要素是时间反演对称性以及将第一定律应用于一个主体对系统做功的情形。无需关于随机或马尔可夫行为的进一步假设，也不需要主方程或经典相空间图景。这些非平衡关系的简单性和普遍性得到了证明，为物理学提供了非常简单的见解。
