  Active galactic nuclei (AGN) are extremely variable in the X-ray band down to
very short timescales. However, the driver behind the X-ray variability is
still poorly understood. Previous results suggest that the hot corona
responsible for the primary Comptonized emission observed in AGN is expected to
play an important role in driving the X-ray variability. In this work, we
investigate the connection between the X-ray amplitude variability and the
coronal physical parameters; namely, the temperature ($kT$) and optical depth
($\tau$). We present the spectral and timing analysis of 46 {\it NuSTAR}
observations corresponding to a sample of 20 AGN. For each source, we derived
the coronal temperature and optical depth through X-ray spectroscopy and
computed the normalized excess variance for different energy bands on a
timescale of $10$ ks. We find a strong inverse correlation between $kT$ and
$\tau$, with correlation coefficient of $r<-0.9$ and negligible null
probability. No clear dependence was found among the temperature and physical
properties, such as the black hole mass or the Eddington ratio. We also see
that the observed X-ray variability is not correlated with either the coronal
temperature or optical depth under the thermal equilibrium assumption, whereas
it is anticorrelated with the black hole mass. These results can be interpreted
through a scenario where the observed X-ray variability could primarily be
driven by variations in the coronal physical properties on a timescale of less
than $10$~ks; whereas we assume thermal equilibrium on such timescales in this
work, given the capability of the currently available hard X-ray telescopes.
Alternatively, it is also possible that the X-ray variability is mostly driven
by the absolute size of the corona, which depends on the supermassive black
hole mass, rather than resulting from any of its physical properties.
