对“在没有可观测海流的情况下推断破坏的细致平衡”的评论
Comment on "Inferring broken detailed balance in the absence of observable currents"
摘要：
在本回复中，我们解决了“关于在没有可观测电流的情况下推断破坏的细致平衡的评论”[arXiv：2112.08978v1]中提出的明显差异。我们强调，非瞬时的过渡路径起源于选择的抽取过程非本地的时间，在我们原来的工作中描述的抽取过程，这与时间反转的通勤相反。因此，使用这种非局部抽取过程的例子，这确实会引起虚假的时间不可逆性，并不会使我们的主要结果无效，这是严格推导和数学证明的。我们希望这个回答能突出时间序列数据抽取的不同选择的微妙之处，这对于正确理解小系统的热力学至关重要。
英文摘要：
In this reply, we resolve the apparent discrepancy raised in the "Comment on Inferring broken detailed balance in the absence of observable currents" [arXiv:2112.08978v1]. We stress that the non-instantaneous transition paths originate from the choice of a decimation process non-local in time, in contrast to the decimation process described in our original work, which commutes with time-reversal. Therefore, the example using such a non-local decimation procedure, which indeed gives rise to spurious time-irreversibility, does not invalidate our main result, which was rigorously derived and proven mathematically. We hope this reply highlights the subtlety of the different choices for decimating time series data which is pivotal for a correct understanding of the thermodynamics of small systems.
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