Subaşı Y, Hu B L
Maryland Center for Fundamental Physics and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jan;85(1 Pt 1):011112. doi: 10.1103/PhysRevE.85.011112. Epub 2012 Jan 6.
In this paper we present a first-principles analysis of the nonequilibrium work distribution and the free energy difference of a quantum system interacting with a general environment (with arbitrary spectral density and for all temperatures) based on a well-understood microphysics (quantum Brownian motion) model under the conditions stipulated by the Jarzynski equality [Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)] and Crooks' fluctuation theorem [Crooks, Phys. Rev. E 60, 2721 (1999)] (in short, fluctuation theorems, FTs). We use the decoherent histories conceptual framework to explain how the notion of trajectories in a quantum system can be made viable and use the environment-induced decoherence scheme to assess the strength of noise that could provide sufficient decoherence to warrant the use of trajectories to define work in open quantum systems. From the solutions to the Langevin equation governing the stochastic dynamics of such systems we were able to produce formal expressions for these quantities entering in the FTs and from them prove explicitly the validity of the FTs at the high temperature limit. At low temperatures our general results would enable one to identify the range of parameters where FTs may not hold or need be expressed differently. We explain the relation between classical and quantum FTs and the advantage of this microphysics open-system approach over the phenomenological modeling and energy-level calculations for substitute closed quantum systems.
在本文中，我们基于一个在雅津斯基等式[雅津斯基，《物理评论快报》78, 2690 (1997)]和克鲁克斯涨落定理[克鲁克斯，《物理评论E》60, 2721 (1999)]（简称为涨落定理，FTs）所规定条件下已被充分理解的微观物理（量子布朗运动）模型，对与一般环境（具有任意谱密度且适用于所有温度）相互作用的量子系统的非平衡功分布和自由能差进行了第一性原理分析。我们使用退相干历史概念框架来解释量子系统中轨迹概念如何变得可行，并使用环境诱导退相干方案来评估噪声强度，该噪声强度可为开放量子系统中使用轨迹来定义功提供足够的退相干。从描述此类系统随机动力学的朗之万方程的解中，我们能够得出FTs中这些量的形式表达式，并由此明确证明FTs在高温极限下的有效性。在低温下，我们的一般结果将使人们能够确定FTs可能不成立或需要以不同方式表述的参数范围。我们解释了经典FTs与量子FTs之间的关系，以及这种微观物理开放系统方法相对于替代封闭量子系统的唯象建模和能级计算的优势。
