According to thermodynamics, the inevitable increase of entropy allows the past to be distinguished from the future. From this perspective, any clock must incorporate an irreversible process that allows this flow of entropy to be tracked. In addition, an integral part of a clock is a clockwork, that is, a system whose purpose is to temporally concentrate the irreversible events that drive this entropic flow, thereby increasing the accuracy of the resulting clock ticks compared to counting purely random equilibration events. In this article, we formalize the task of autonomous temporal probability concentration as the inherent goal of any clockwork based on thermal gradients. Within this framework, we show that a perfect clockwork can be approximated arbitrarily well by increasing its complexity. Furthermore, we combine such an idealized clockwork model, comprised of many qubits, with an irreversible decay mechanism to showcase the ultimate thermodynamic limits to the measurement of time.

中文翻译：

---

自主时间概率集中度：钟表和热力学第二定律

根据热力学，熵的必然增加使过去与未来有所区别。从这个角度来看，任何时钟都必须包含一个不可逆的过程，以允许跟踪这种熵流。此外，时钟的组成部分是发条，即一种系统，其目的是暂时集中驱动该熵流的不可逆事件，从而与计算纯随机平衡事件相比，提高了产生的时钟滴答的准确性。在本文中，我们形式化了自主时间概率集中的任务作为任何基于热梯度的发条的固有目标。在此框架内，我们表明，通过增加复杂度，可以完美地近似完美的发条。此外，我们将这种理想化的发条模型（包含许多量子位）与不可逆的衰减机制结合在一起，展示了对时间测量的最终热力学极限。