Quantum clocks and thermodynamics

最近在量子热力学方面的研究表明，我们通过物理时钟精确测量时间的能力与热力学时间箭头（就熵的增加而言）之间存在定量联系。进一步探索这种联系将是有趣的，超越最初研究的特定模型，以及研究使用显式量子时钟来测量时间的更广泛含义（例如相对于时钟时间的有效动力学）。另外两个相关的问题是：如果时间是离散的，比如在量子细胞自动机（量子计算的局部平移不变模型）中，平衡和热化是如何受到影响的？我们是否可以用量子时钟来创造两种不同时间顺序的测量的叠加，这样的结果就不能用经典的时间顺序的混合来解释了？

Recent work in quantum thermodynamics has shown a quantitative connection between our ability to measure time precisely via a physical clock, and the thermodynamic arrow of time (in terms of increasing entropy). It would be interesting to explore this connection further, going beyond the particular model studied initially, as well as to investigate the broader implications of using explicit quantum clocks to measure time (such as the effective dynamics relative to the clock-time). Two additional related questions are: How are equilibration and thermalisation affected if time is discrete, such as in a quantum cellular automata (a local translationally invariant model of quantum computation)? Could we use a quantum clock to create a superposition of two different time-orderings of measurements, such that the results could not be explained by a classical mixture of time-orderings?