Allahverdyan Armen E, Hovhannisyan Karen V, Janzing Dominik, Mahler Guenter
Yerevan Physics Institute, Alikhanian Brothers Street 2, Yerevan 375036, Armenia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Oct;84(4 Pt 1):041109. doi: 10.1103/PhysRevE.84.041109. Epub 2011 Oct 10.
We study dynamic cooling, where an externally driven two-level system is cooled via reservoir, a quantum system with initial canonical equilibrium state. We obtain explicitly the minimal possible temperature T(min)>0 reachable for the two-level system. The minimization goes over all unitary dynamic processes operating on the system and reservoir and over the reservoir energy spectrum. The minimal work needed to reach T(min) grows as 1/T(min). This work cost can be significantly reduced, though, if one is satisfied by temperatures slightly above T(min). Our results on T(min)>0 prove unattainability of the absolute zero temperature without ambiguities that surround its derivation from the entropic version of the third law. We also study cooling via a reservoir consisting of N≫1 identical spins. Here we show that T(min)∝1/N and find the maximal cooling compatible with the minimal work determined by the free energy. Finally we discuss cooling by reservoir with an initially microcanonic state and show that although a purely microcanonic state can yield the zero temperature, the unattainability is recovered when taking into account imperfections in preparing the microcanonic state.
我们研究动态冷却，即通过热库（一个具有初始正则平衡态的量子系统）来冷却一个外部驱动的两能级系统。我们明确得到了两能级系统可达到的最小可能温度(T_{min}>0)。最小化过程遍历作用于系统和热库的所有幺正动态过程以及热库的能谱。达到(T_{min})所需的最小功随(1/T_{min})增长。不过，如果满足于略高于(T_{min})的温度，这种功的消耗可以显著降低。我们关于(T_{min}>0)的结果证明了绝对零度的不可达性，避免了从熵形式的第三定律推导绝对零度时所存在的模糊性。我们还研究了通过由(N\gg1)个相同自旋组成的热库进行冷却的情况。在此我们表明(T_{min}\propto1/N)，并找到了与由自由能确定的最小功兼容的最大冷却量。最后，我们讨论了具有初始微正则态的热库的冷却情况，并表明尽管纯微正则态可以达到零温度，但考虑到制备微正则态时的不完美性，不可达性又会恢复。
