We discuss how to use correlations between different physical observables to improve recently obtained thermodynamics bounds, notably the fluctuation-response inequality and the thermodynamic uncertainty relation (TUR). We show that increasing the number of measured observables will always produce a tighter bound. This tighter bound becomes particularly useful if one of the observables is a conserved quantity, whose expectation is invariant under a given perturbation of the system. For the case of the TUR, we show that this applies to any function of the state of the system. The resulting correlation TUR takes into account the correlations between a current and a noncurrent observable, thereby tightening the TUR. We demonstrate our finding on a model of the ${\mathrm{F}}_1$-ATPase molecular motor, a Markov jump model consisting of two rings and transport through a two-dimensional channel. We find that the correlation TUR is significantly tighter than the TUR and can be close to an equality even far from equilibrium.

中文翻译：

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使用相关性改进热力学界限

我们讨论了如何使用不同物理观测值之间的相关性来改进最近获得的热力学界限，特别是波动响应不等式和热力学不确定性关系 (TUR)。我们表明，增加可测量的可观察量的数量总是会产生更严格的界限。如果其中一个可观察量是守恒量，并且在给定的系统扰动下其期望是不变的，则这种更严格的界限变得特别有用。对于 TUR 的情况，我们表明这适用于系统状态的任何函数。由此产生的相关性 TUR 考虑了当前和非当前可观测值之间的相关性，从而收紧了 TUR。我们在一个模型上展示了我们的发现${\mathrm{F}}_1$-ATPase 分子马达，一个由两个环组成并通过二维通道运输的马尔可夫跳跃模型。我们发现相关性 TUR 明显比 TUR 更紧密，并且即使远离平衡也可以接近等式。