次高斯和次指数波动响应不等式
Sub-Gaussian and subexponential fluctuation-response inequalities
摘要：
引入了次高斯分布和次指数分布，并将其应用于研究非平衡状态下的波动-响应关系。对任意次高斯或次指数物理量的期望值之差，根据其次高斯或次指数范数建立了一个界。在此基础上，我们发现两个态之间的熵差受这些态的能量涨落的限制。此外，我们得到了不同制度的热力学不确定性关系的广义版本。有关我们的结果在实验环境中的应用的操作问题也得到解决，和nonasymptomatic边界上所产生的误差使用的样本平均值，而不是期望值在我们的波动响应不等式。
英文摘要：
Sub-Gaussian and subexponential distributions are introduced and applied to study the fluctuation-response relation out of equilibrium. A bound on the difference in expected values of an arbitrary sub-Gaussian or subexponential physical quantity is established in terms of its sub-Gaussian or subexponential norm. Based on that, we find that the entropy difference between two states is bounded by the energy fluctuation in these states. Moreover, we obtain generalized versions of the thermodynamic uncertainty relation in different regimes. Operational issues concerning the application of our results in an experimental setting are also addressed, and nonasymptotic bounds on the errors incurred by using the sample mean instead of the expected value in our fluctuation-response inequalities are derived.
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