从单次激发到具有有界工作波动的一般工作提取
From single-shot to general work extraction with bounded fluctuations in work
摘要：
在热力学的标准框架中，过程中产生或消耗的功是一个随机变量，其平均值受系统自由能变化的限制。这个功的计算不考虑其波动的大小。我们发现，在某些过程中，如可逆冷却，工作的波动可以发散。小型或脆弱的热机可能无法应对大的波动。因此，目前的重点是纳米尺度的热力学，我们分析如何修改热力学效率率时，平均波动的大小受到限制。当功的涨落以给定的量c为界时，我们量化了任何态的功含量和形成功。通过改变c，我们在标准自由能c =无穷大和最小自由能c = 0之间进行插值，定义在单次热力学的上下文中。我们推导出平均功与其涨落之间的基本关系，并探讨了涨落束缚时状态变换的不可逆性和偏序性的出现。我们还研究了具有约束涨落的单量子比特热机模型的效率，并导出了对卡诺效率的修正。
英文摘要：
In the standard framework of thermodynamics the work produced or consumed in a process is a random variable whose average value is bounded by the change in the free energy of the system. This work is calculated without regard for the size of its fluctuations. We find that in some processes, such as reversible cooling, the fluctuations of the work can diverge. Small or fragile thermal machines may be unable to cope with large fluctuations. Hence, with the present focus on nano- scale thermodynamics, we analyse how thermodynamic efficiency rates are modified when the size of the fluctuations around the average is restricted. We quantify the work content and work of formation of any state when the work fluctuations are bounded by a given amount c. By varying c we interpolate between the standard free energy c = infinity and the min-free energy c = 0, defined in the context of single-shot thermodynamics. We derive fundamental relations between average work and its fluctuations, and explore the emergence of irreversibility and partial order on state transformations when bounding fluctuations. We also study the efficiency a single qubit thermal engine model with constrained fluctuations, and derive the corrections to the Carnot efficiency.
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