  We develop a general phenomenology describing the interplay between coherent
and incoherent dynamics in ferromagnetic insulators. Using the Onsager
reciprocity and Neumann's principle, we derive expressions for the local
thermomagnonic torques exerted by thermal magnons on the order-parameter
dynamics and the reciprocal pumping processes, which are in close analogy to
the spin-transfer torque and spin pumping at metallic interfaces. Our formalism
is applicable to general long-wavelength dynamics and, although here we
explicitly focus on ferromagnetic insulators possessing U(1) symmetry, our
approach can be easily extended to other classes of magnetic materials. As an
illustrative example, we apply our theory to investigate a domain wall floating
over a spin superfluid, whose dynamics is triggered thermally at the system's
edge. Our results demonstrate that the local pumping of coherent spin dynamics
by a thermal magnon gas offers an alternative route - with no need for
conducting components and thus devoid of Ohmic losses - for the control and
manipulation of topological solitons.
