Clock synchronization is critically important in positioning, navigation and timing systems. While its performance has been intensively studied in a wide range of disciplines, much less is known for the fundamental thermodynamics of clock synchronization‒what limits the precision and how to optimize the energy cost for clock synchronization. Here, we report the first experimental investigation of two stochastic autonomous clocks synchronization, unveiling the thermodynamic relation between the entropy cost and clock synchronization in an open cavity optomechanical system. Two interacting clocks are synchronized spontaneously owing to the disparate decay rates of hybrid modes by engineering the controllable cavity-mediated dissipative coupling. The measured dependence of the degree of synchronization on the overall entropy cost exhibits an unexpected non-monotonic characteristic, while the relation between the degree of synchronization and the entropy cost for the synchronization is monotonically decreasing. The investigation of transient dynamics of clock synchronization exposes a trade-off between energy and time consumption. Our results demonstrate the possibility of clock synchronization in an effective linear system, reveal the fundamental relation between clock synchronization and thermodynamics, and have a great potential for precision measurements, distributed quantum networks, and biological science.

中文翻译：

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时钟同步的异常热力学成本


时钟同步在定位、导航和授时系统中至关重要。虽然其性能已在广泛的学科中得到深入研究，但人们对时钟同步的基本热力学知之甚少——什么限制了精度以及如何优化时钟同步的能源成本。在这里，我们报告了两个随机自主时钟同步的首次实验研究，揭示了开腔光机械系统中熵成本和时钟同步之间的热力学关系。通过设计可控腔介导的耗散耦合，由于混合模式的不同衰减率，两个相互作用的时钟自发同步。测量的同步度对总熵成本的依赖性表现出意想不到的非单调特性，而同步度与同步的熵成本之间的关系是单调递减的。对时钟同步瞬态动态的研究揭示了能量和时间消耗之间的权衡。我们的结果证明了有效线性系统中时钟同步的可能性，揭示了时钟同步与热力学之间的基本关系，并且在精密测量、分布式量子网络和生物科学方面具有巨大潜力。