  Long-term observations have shown that black hole X-ray binaries exhibit
strong, aperiodic variability on time-scales of a few milliseconds to seconds.
The observed light curves display various characteristic features like a
log-normal distribution of flux and a linear rms-flux relation, which indicate
that the underlying variability process is stochastic in nature. It is also
thought to be intrinsic to accretion. This variability has been modelled as
inward propagating fluctuations of mass accretion rate, although the physical
process driving the fluctuations remains puzzling. In this work, we analyse
five exceptionally long duration general relativistic magnetohydrodynamic
(GRMHD) simulations of optically thin, geometrically thick, black hole
accretion flows to look for hints of propagating fluctuations in the simulation
data. We find that the accretion profiles from these simulations do show
evidence for inward propagating fluctuations below the viscous frequency by
featuring strong radial coherence and positive time lags when comparing smaller
to larger radii, although these time lags are generally shorter than the
viscous time-scale and frequency independent. Our simulations also support the
notion that the fluctuations in $\dot{M}$ build up in a multiplicative manner,
as the simulations exhibit linear rms-mass flux relations, as well as
log-normal distributions of their mass fluxes. When combining the mass fluxes
from the simulations with an assumed emissivity profile, we additionally find
broad agreement with observed power spectra and time lags, including a recovery
of the frequency dependency of the time lags.
