Cross-Spectral Witness for Hidden Nonequilibrium Beyond the Scalar Ceiling

TL;DR

This paper introduces a cross-spectral method to detect hidden nonequilibrium forces in systems where scalar observables fail, providing a new way to identify underlying drives and entropy production.

Contribution

It derives a closed-form cross-spectral witness that reveals hidden drives in multichannel systems, surpassing scalar limitations and applicable under specific structural assumptions.

Findings

The cross-spectral witness is strictly positive at all nonzero cross-couplings.

Under channel-separable structure, the witness cancels scalar reductions, exposing hidden spectra.

In one-way coupled systems, the witness estimates the total entropy production rate.

Abstract

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.