  We theoretically establish mutual relations among magnetic momentum, heat,
and fluctuations of propagating magnons in a ferromagnetic insulating junction
in terms of noise and the bosonic Wiedemann-Franz (WF) law. Using the
Schwinger-Keldysh formalism, we calculate all transport coefficients of a noise
spectrum for both magnonic spin and heat currents, and establish Onsager
relations between the thermomagnetic currents and the zero-frequency noise.
Making use of the magnonic WF law and the Seebeck coefficient in the
low-temperature limit, we theoretically discover universal relations, i.e.
being independent of material parameters, for both the nonequilibrium and
equilibrium noise, and show that each noise is described solely in terms of
thermal conductance. Finally, we introduce a magnonic spin-analog of the Fano
factor, noise-to-current ratio, and demonstrate that the magnonic spin-Fano
factor reduces to a universal value in the low-temperature limit and it remains
valid even beyond a linear response regime.
