For a thought experiment concerning the mixing of two classical gases, Gibbs concluded that the work that can be extracted from mixing is determined by whether or not the gases can be distinguished by a semi-permeable membrane; that is, the mixing work is a discontinuous function of how similar the gases are. Here we describe an optomechanical setup that generalises Gibbs' thought experiment to partially distinguishable quantum gases. Specifically, we model the interaction between a polarising beamsplitter, that plays the role of a semi-permeable membrane, and two photon gases of non-orthogonal polarisation. We find that the work arising from the mixing of the gases is related to the potential energy associated with the displacement of the microscopic membrane, and we derive a general quantum mixing work expression, valid for any two photon gases with the same number distribution. The quantum mixing work is found to change continuously with the distinguishability of the two polarised gases. In addition, fluctuations of the work on the microscopic membrane become important, which we calculate for Fock and thermal states of the photon gases. Our findings generalise Gibbs' mixing to the quantum regime and open the door for new quantum thermodynamic (thought) experiments with quantum gases with non-orthogonal polarisations and microscopic pistons that can distinguish orthogonal polarisations.

中文翻译：

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部分可区分光子与偏振分束膜的吉布斯混合

对于关于两种经典气体混合的思想实验，Gibbs 得出结论，可以从混合中提取的功取决于是否可以通过半透膜区分气体；也就是说，混合功是气体相似程度的不连续函数。在这里，我们描述了一种光机械装置，它将吉布斯的思想实验推广到部分可区分的量子气体。具体来说，我们模拟了起半透膜作用的偏振分束器和两种非正交偏振光子气体之间的相互作用。我们发现气体混合产生的功与微观膜位移相关的势能有关，我们推导出一般的量子混合功表达式，对具有相同数量分布的任意两种光子气体有效。发现量子混合功随着两种极化气体的可区分性而不断变化。此外，微观膜上工作的波动变得很重要，我们计算了光子气体的 Fock 和热状态。我们的研究结果将吉布斯的混合推广到量子体系，并为新的量子热力学（思想）实验打开了大门，这些实验具有非正交极化的量子气体和可以区分正交极化的微观活塞。我们计算了光子气体的 Fock 和热态。我们的研究结果将吉布斯的混合推广到量子体系，并为新的量子热力学（思想）实验打开了大门，这些实验具有非正交极化的量子气体和可以区分正交极化的微观活塞。我们计算了光子气体的 Fock 和热态。我们的研究结果将吉布斯的混合推广到量子体系，并为新的量子热力学（思想）实验打开了大门，这些实验具有非正交极化的量子气体和可以区分正交极化的微观活塞。