  A mass of dark matter halo is commonly defined as the spherical over-density
(SO) mass with respect to a reference density, whereas the time evolution of an
SO mass can be affected by the redshift evolution of the reference density as
well as the physical mass accretion around halos. In this study, we directly
measure the amount of pseudo evolution of the SO masses of cluster-sized halos
by the changes in the reference density from a time series of $N$-body
simulations for the first time. We find that the $52\pm19\%$ difference in the
virial SO masses between $z=0$ and $1$ can be accounted for by the pseudo
evolution of clusters with a virial mass of $10^{14}\, h^{-1}M_{\odot}$ at
$z=0$. The amount of pseudo evolution is found to be correlated with the age
and density environment of a galaxy cluster. The stacked mass density profiles
of cluster-sized halos with a greater amount of pseudo evolution in the SO mass
shows the higher concentration ${\it and}$ greater linear bias parameter that
is a counter-example of the known secondary halo bias due to concentration on
the scale of clusters. We discuss how more concentrated clusters can show
larger clustering amplitudes than their less concentrated counterparts and
argue that the presence of rich filamentary structures plays a critical role in
determining the linear halo bias of galaxy clusters.
