Lucente et al. proved that no time-irreversibility measure can detect departure from equilibrium in a scalar Gaussian time series from a linear system. We show that a second observed channel sharing the same hidden driver overcomes this impossibility: the cross-spectral block, structurally inaccessible to any single-channel measure, provides qualitatively new detectability. Under the diagonal null hypothesis, the cross-spectral detectability coefficient $\Scross$ (the leading quartic-order cross contribution) is \emph{exactly} independent of the observed timescales -- a cancellation governed solely by hidden-mode parameters -- and remains strictly positive at exact timescale coalescence, where all single-channel measures vanish. The mechanism is geometric: the cross spectrum occupies the off-diagonal subspace of the spectral matrix, orthogonal to any diagonal null and therefore invisible in any single-channel reduction. For the one-way coupled Ornstein--Uhlenbeck counterpart, the entropy production rate (EPR) satisfies $\EPRtot=α_2λ^2$ exactly; under this coupling geometry, $\Scross>0$ certifies $\EPRtot>0$, linking observable cross-spectral structure to full-system dissipation via $\EPRtot^{\,2}\propto\Scross$. Finite-sample simulations predict a quantitative detection-threshold split testable with dual colloidal probes and multisite climate stations.

翻译：Lucente等人证明，对于线性系统中标量高斯时间序列，任何时间不可逆性度量都无法检测到其偏离平衡态。我们表明，共享同一隐藏驱动 的双通道观测可克服这一不可能性：交叉谱块在结构上对任何单通道度量均不可及，提供了定性全新的可检测性。在对角线零假设下，交叉谱可检测系数 $\Scross$（主导的四阶交叉贡献）\emph{精确}独立于观测时间尺度——这一抵消仅由隐藏模式参数决定——并在时间尺度完全重合时严格保持正值，而此时所有单通道度量均消失。其机制是几何性的：交叉谱占据谱矩阵的非对角子空间，与任何对角线零假设正交，因此在任何单通道约化中均不可见。对于单向耦合的Ornstein--Uhlenbeck对应系统，熵产生率（EPR）精确满足 $\EPRtot=α_2λ^2$；在该耦合几何下，$\Scross>0$ 保证 $\EPRtot>0$，通过 $\EPRtot^{\,2}\propto\Scross$ 将可观测的交叉谱结构与全系统耗散联系起来。有限样本模拟预测了可量化的检测阈值分裂，可通过双胶体探针及多站点气候站进行实验验证。