Abstract Thermodynamic quantities of small systems fluctuate and have to be characterised by their appropriate probability distributions. Within the two-point energy measurement prescription, the distribution of work in a quantum system can be derived from the transition probability from initial to final energy. We consider a simple yet representative model system starting in thermodynamic equilibrium and driven by an external force, and compare two different numerical techniques to determine this transition probability with respect to accuracy and numerical effort. In addition, we perform a semi-classical analysis of the process using the WKB approximation. The results agree well with the numerically exact values if Airy-tails modelling the tunnelling into classically forbidden regions of phase space are properly taken into account.

中文翻译：

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驱动量子系统中的工作统计和能量转换

摘要 小系统的热力学量是波动的，必须用它们适当的概率分布来表征。在两点能量测量公式中，量子系统中功的分布可以从初始能量到最终能量的跃迁概率推导出来。我们考虑一个简单但具有代表性的模型系统，该系统从热力学平衡开始并由外力驱动，并比较两种不同的数值技术，以确定在精度和数值努力方面的这种转变概率。此外，我们使用 WKB 近似对该过程进行了半经典分析。如果适当地考虑对进入相空间经典禁止区域的隧道进行建模的 Airy-tails，则结果与数值上的精确值非常吻合。