Fluctuation theory for statistical thermal drives

Develop a fluctuation theory for statistical drives, including the noise generated by a real temperature gradient in bosonic thermal transport.

Background

The paper analyzes a force-driven protocol for magnons but explains that a real temperature gradient is a statistical drive rather than a mechanical force. Consequently, the anomalous-velocity treatment used for the force-driven noise does not provide the fluctuation-level description of thermal transport under a temperature gradient. The missing theory is also relevant to finite-q statistical-magnetization fluctuations and the associated heat-channel continuation.

References

And the fluctuation theory of statistical drives, which would underwrite a real temperature gradient at the level of noise, does not yet exist; it is delimited in Sec.~\ref{sec:driven}, together with the finite-$q$ statistical-magnetization fluctuation and the $O(q{2})$ counting of the transport-magnetization cross term, and belongs to the heat-channel continuation.

— Topology is not silent in the transport noise of multiband bosons  (2608.18527 - Wang et al., 19 Aug 2026) in Section 5, “The driven protocol does not work,” and Section 14, “Discussion”