# Cross-Spectral Witness for Hidden Nonequilibrium Beyond the Scalar Ceiling

arXiv: https://arxiv.org/abs/2604.03775 · HTML: https://mlsanity.com/paper/2604.03775/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 46 references that are in the map.
- First posted on arXiv 4 Apr 2026.

## Builds on (most cited first, 2 of 2)

- [Decomposing Thermodynamic Dissipation of Linear Langevin Systems via Oscillatory Modes and Its Application to Neural Dynamics](https://mlsanity.com/paper/2312.03489/) (2023)
- [Entropy production of Multivariate Ornstein-Uhlenbeck processes correlates with consciousness levels in the human brain](https://mlsanity.com/paper/2207.05197/) (2022)

## Abstract (arXiv)

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.