Fleming C H, Hu B L, Roura Albert
Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jul;88(1):012102. doi: 10.1103/PhysRevE.88.012102. Epub 2013 Jul 3.
The fluctuation-dissipation relation is usually formulated for a system interacting with a heat bath at finite temperature, and often in the context of linear response theory, where only small deviations from the mean are considered. We show that for an open quantum system interacting with a nonequilibrium environment, where temperature is no longer a valid notion, a fluctuation-dissipation inequality exists. Instead of being proportional, quantum fluctuations are bounded below by quantum dissipation, whereas classically the fluctuations vanish at zero temperature. The lower bound of this inequality is exactly satisfied by (zero-temperature) quantum noise and is in accord with the Heisenberg uncertainty principle, in both its microscopic origins and its influence upon systems. Moreover, it is shown that there is a coupling-dependent nonequilibrium fluctuation-dissipation relation that determines the nonequilibrium uncertainty relation of linear systems in the weak-damping limit.
涨落耗散关系通常是针对在有限温度下与热库相互作用的系统来表述的，并且常常是在线性响应理论的背景下，其中只考虑相对于均值的小偏差。我们表明，对于与非平衡环境相互作用的开放量子系统，在温度不再是一个有效概念的情况下，存在一个涨落耗散不等式。量子涨落并非成比例关系，而是由量子耗散界定下限，而在经典情况下，涨落在零温度时消失。这个不等式的下限恰好由（零温度）量子噪声满足，并且在微观起源及其对系统的影响方面都符合海森堡不确定性原理。此外，结果表明存在一个依赖于耦合的非平衡涨落耗散关系，它决定了弱阻尼极限下线性系统的非平衡不确定性关系。
