Partial observation is a pervasive obstacle in nonequilibrium physics: coarse graining may absorb hidden forcing into an apparently equilibrium-like reduced description, so a driven system can look reversible through the only variables one can measure. For scalar Gaussian observables of linear stochastic systems, no time-irreversibility statistic can detect the underlying drive. The Lucente--Crisanti ceiling constrains what one channel carries; what two channels carry is a different question, with a sharp closed-form answer. Two simultaneously observed channels retain an off-diagonal cross-spectral sector inaccessible to any scalar reduction; under channel-separable multiplicative structure the observed-channel response factors cancel identically, leaving a closed-form cross-spectral witness controlled only by the hidden spectrum, the loadings, and the innovation scales, strictly positive at every nonzero cross-coupling including at exact timescale coalescence where every scalar reduction is blind. Within general CSM this certifies shared hidden-sector drive; under the additional one-way coupling assumption the witness identifies the total entropy production rate at leading order with a square-root scaling.

翻译：局部观测是非平衡态物理中普遍存在的障碍：粗粒化可能将隐藏驱动吸收进看似平衡态的约化描述中，使得受驱系统通过唯一可测量的变量呈现可逆性。对于线性随机系统的标量高斯可观测量，任何时间不可逆性统计量都无法检测到潜在的驱动。卢琴特-克里桑蒂上限约束了单个通道所承载的信息；而两个通道所承载的信息则是另一个问题，具有明确的闭式解。两个同步观测通道保留了对角交叉谱区域，该区域无法通过任何标量约化方式获取；在通道可分离乘性结构下，观测通道的响应因子相互抵消，仅由隐藏谱、载荷因子和创新尺度控制的闭式交叉谱见证严格为正，且在所有非零交叉耦合处（包括精确时间尺度重合处——此时所有标量约化均为盲区）均保持这一特性。在一般交叉谱乘性结构框架下，这证实了共享隐藏扇区驱动的存在；在附加单向耦合假设下，该见证可识别主导阶的熵产生率，并呈现平方根标度关系。