Origin and scope of the spontaneous cancellation mechanism in equal-time correlators

Characterize and explain the spontaneous cancellation mechanism that renders equal-time correlators of conserved densities independent of cutoff parameters in the studied examples, determine its mathematical and physical origin, and ascertain why this mechanism appears to be specific to equal-time correlators.

Background

Throughout several examples, the authors find that while equal-time correlators of frame-dependent variables (e.g., velocity) depend on cutoff scales, the equal-time correlators of conserved densities match standard nonrelativistic results and become independent of the cutoff when the stochastic and deterministic cutoff scales coincide.

They attribute this to a spontaneous cancellation mechanism but expressly state that they do not yet understand it. Clarifying this mechanism would improve understanding of the robustness of predictions and delineate when such cancellations occur.

References

This is due to a spontaneous cancellation mechanism that we do not fully understand yet, and which seems to be specific to equal-time correlators (it will surely break down in correlators computed at non-equal times).

— First-order relativistic hydrodynamics with an information current  (2401.13852 - Gavassino et al., 2024) in Conclusions (Section IX)

Our results also raise several new questions. We have defined causation as the static ($\omega \to 0$) limit of the Kubo response formula; at finite frequency, descendant fields may again contribute, and to what extent the suppression persists would be worthwhile to investigate.

— Correlation versus Causation in Quantum Criticality  (2608.12770 - Wichmann et al., 13 Aug 2026) in Discussion