Quantum clocks and thermodynamics

量子热力学的最新研究表明，我们通过物理时钟精确测量时间的能力与时间的热力学箭头（熵增加）之间存在定量联系。进一步探索这种联系，超越最初研究的特定模型，以及研究使用显式量子钟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）将是有趣的。另外两个相关的问题是：如果时间是离散的，例如在量子细胞自动机（量子计算的局部几何不变模型）中，平衡和热化是如何受到影响的？我们能不能用量子钟来创造两种不同时间顺序的测量叠加，使得结果不能用经典的时间顺序混合来解释？

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?