In the standard framework of thermodynamics work is a random variable whose average is bounded by the change in free energy of the system. This average work is calculated without regard for the size of its fluctuations. We show that for some processes, such as reversible cooling, the fluctuations in work diverge. Realistic thermal machines may be unable to cope with arbitrarily large fluctuations. Hence, it is important to understand how thermodynamic efficiency rates are modified by bounding fluctuations. We quantify the work content and work of formation of arbitrary finite dimensional quantum states when the fluctuations in work are bounded by a given amount $c$. By varying $c$ we interpolate between the standard and min free energies. We derive fundamental trade-offs between the magnitude of work and its fluctuations. As one application of these results, we derive the corrected Carnot efficiency of a qubit heat engine with bounded fluctuations.
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机译：在热力学的标准框架中，工作是一个随机变量，其平均值受系统自由能的变化限制。计算该平均功时不会考虑其波动幅度。我们表明，对于某些过程（例如可逆冷却），工作波动会有所不同。现实的热力机器可能无法应对任意大的波动。因此，重要的是要了解如何通过边界波动来改变热力学效率。当工作的波动以给定的量$ c $为边界时，我们量化工作内容和形成任意有限维量子态的工作。通过改变$ c $，我们可以在标准和最小自由能之间进行插值。我们得出工作量及其波动之间的基本权衡。作为这些结果的一种应用，我们推导了具有有限波动的量子位热机的校正卡诺效率。
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