本文综述了热力学不确定性关系(TUR)的最新研究进展，涵盖了从经典到量子系统，从稳态到周期驱动系统等多个方面。文章深入探讨了TUR在分子马达、生物分子过程、热机等领域的应用，并讨论了其在生物化学振荡、量子热力学等新兴方向的意义。此外，文章还总结了各种形式的TUR，包括针对电流、首次通过时间、熵产生等不同物理量的限制，为理解非平衡系统的行为提供了理论框架。文章旨在为读者提供关于热力学不确定性关系研究的全面概述。

🔬热力学不确定性关系（TUR）为非平衡系统中的可观测量的涨落设定了基本限制，这些限制与熵产生相关联，为理解这些系统的行为提供了理论框架。

🔄TUR的研究已从稳态系统扩展到周期性驱动系统，并考虑了时间反转对称性破缺的影响，揭示了不同条件下涨落的普遍限制。

🧬TUR在分子马达、生物分子过程等生物系统中得到了广泛应用，研究表明，TUR可以限制生物过程的效率和精度，例如生物化学振荡的相干性。

🌡️量子系统中的TUR研究也取得了进展，包括对量子热电装置、量子输运等领域的研究，揭示了量子效应如何影响热力学不确定性关系。

⏱️研究者们提出了针对不同物理量（如首次通过时间、电流等）的TUR，并进一步研究了这些关系的适用性和局限性，为理解非平衡系统的涨落提供了更多工具。

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