  Casimir physics covers a wealth of phenomena where forces between macroscopic
objects are induced by long range fluctuations of either classical or quantum
origin. Fluctuations of the quantum electrodynamic vacuum epitomize this type
of physics, but such fluctuation induced forces arise in a wide range of
systems. Here we present a surprisingly never anticipated example of
fluctuation induced radiation forces, stemming from spatially long ranged
mesoscopic coherent fluctuations of light propagating in random media. Quite
remarkably, spatially coherent light fluctuations can be thoroughly described
by a hydrodynamic Langevin approach, where a properly tailored noise accounts
for mesoscopic coherent effects. The light flow depends on two parameters only,
the diffusion coefficient $D$ and the mobility $\sigma$, otherwise related by a
Einstein relation. The mapping we present between coherent light flow and out
of equilibrium hydrodynamics is easily generalisable to a large class of
quantum or classical wave problems. A clear asset of this type of approach is
in its dependence upon two parameters only thus making it a candidate to
efficient machine learning algorithms. Moreover, the strength of these coherent
fluctuating forces depends on a single and easily tunable dimensionless
conductance $g$ -- analog of electronic conductance -- which encapsulates both
the geometry and the scattering properties of the random medium. Hence coherent
multiple light scattering offers setups where fluctuation induced forces are
significantly enhanced compared to other known situations. The scarcity of
measurable non equilibrium phenomena makes the present proposal particularly
relevant to experimental inspections and applications, e.g. a wide variety of
sensors in soft condensed matter, biophysics and quantum technologies.

Mesoscale and Nanoscale Physics