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.

中文翻译：

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次高斯和次指数波动响应不等式

引入亚高斯分布和亚指数分布，并将其用于研究非平衡状态下的波动-响应关系。根据其次高斯或次指数范数建立任意次高斯或次指数物理量的期望值之差的界限。基于此，我们发现两个状态之间的熵差受到这些状态中能量波动的限制。此外，我们获得了不同状态下热力学不确定性关系的广义形式。还讨论了与在实验环境中应用我们的结果有关的操作问题，并得出了使用样本均值而不是波动响应不等式中的期望值引起的误差的非渐近界限。