Kawamoto Tatsuro, Hatano Naomichi
Department of Physics, The University of Tokyo, Komaba, Meguro, Tokyo 153-8505, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Sep;84(3 Pt 1):031116. doi: 10.1103/PhysRevE.84.031116. Epub 2011 Sep 13.
We study fluctuation theorems for open quantum systems with a non-Markovian heat bath using the approach of quantum master equations and examine the physical quantities that appear in those fluctuation theorems. The approach of Markovian quantum master equations to the fluctuation theorems was developed by Esposito and Mukamel [Phys. Rev. E 73, 046129 (2006)]. We show that their discussion can be formally generalized to the case of a non-Markovian heat bath when the local system is linearly connected to a Gaussian heat bath with the spectrum distribution of the Drude form. We found by numerically simulating the spin-boson model in non-Markovian regime that the "detailed balance" condition is well satisfied except in a strongly nonequilibrium transient situation, and hence our generalization of the definition of the "entropy production" is almost always legitimate. Therefore, our generalization of the fluctuation theorem seems meaningful in wide regions.
我们使用量子主方程的方法研究了具有非马尔可夫热库的开放量子系统的涨落定理，并研究了那些涨落定理中出现的物理量。Esposito和Mukamel [《物理评论E》73, 046129 (2006)] 发展了马尔可夫量子主方程用于涨落定理的方法。我们表明，当局部系统与具有德鲁德形式谱分布的高斯热库线性连接时，他们的讨论可以形式上推广到非马尔可夫热库的情况。我们通过对非马尔可夫区域的自旋玻色子模型进行数值模拟发现，除了在强非平衡瞬态情况下，“细致平衡”条件得到很好的满足，因此我们对“熵产生”定义的推广几乎总是合理的。所以，我们对涨落定理的推广在广泛的区域似乎是有意义的。
