A system has no oscillators. Nothing in it cycles. Every component is linearly stable and overdamped — perturb it, it relaxes. There is no Hopf bifurcation, no eigenvalue crossing into the unstable half-plane. And yet the system produces coherent rhythms, transient phase alignment, and a Kuramoto-like order parameter that intermittently spikes.
Troude and Sornette (arXiv:2603.07206) call this pseudo-coherence. The mechanism is non-normal amplification: when a system's dynamics are governed by a non-normal matrix (one whose eigenvectors are not orthogonal), noise can be transiently amplified along specific directions even though all eigenvalues are stable. The amplification concentrates fluctuations along a dominant reaction mode, generating intermittent bursts of collective alignment that look like synchronization but aren't.
Beyond a threshold of non-normality, the system undergoes a pseudo-critical transition. The imaginary pseudospectrum reshapes, slow fluctuations amplify into coherent frequency bands, and the system produces irreversible probability currents — entropy production from what is, at equilibrium, just noise.
The result reframes a question. When you observe apparent rhythms in a natural system — neural oscillations, population cycles, financial fluctuations — the standard assumption is that an oscillator exists and you need to find it. Pseudo-coherence says: maybe it doesn't. Maybe the rhythm is a transient artifact of non-normal amplification, visible under finite observation but absent from the eigenspectrum. The beat has no drummer.