Comment on "Inferring broken detailed balance in the absence of observable currents"

TL;DR

This paper clarifies a previous debate by emphasizing the importance of the decimation process in analyzing detailed balance and time-reversibility in small systems, reaffirming the validity of their original results.

Contribution

The authors clarify that their original mathematical proof remains valid despite claims of spurious irreversibility caused by non-local decimation procedures.

Findings

Original proof of detailed balance inference is robust

Non-local decimation can produce spurious irreversibility

Correct decimation process is crucial for thermodynamic analysis

Abstract

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.