  The growth of a tissue, which depends on cell-cell interactions and
biologically relevant process such as cell division and apoptosis, is regulated
by a mechanical feedback mechanism. We account for these effects in a minimal
two-dimensional model in order to investigate the consequences of mechanical
feedback, which is controlled by a critical pressure, $p_c$. A cell can only
grow and divide if the pressure it experiences, due to interaction with its
neighbors, is less than $p_c$. Because temperature is an irrelevant variable in
the model, the cell dynamics is driven by self-generated active forces (SGAFs)
that are created by cell division. It is shown that even in the absence of
intercellular interactions, cells undergo diffusive behavior. The SGAF driven
diffusion is indistinguishable from the well-known dynamics of a free Brownian
particle at a fixed finite temperature. When intercellular interactions are
taken into account, we find persistent temporal correlations in the force-force
autocorrelation function ($FAF$) that extends over timescale of several cell
division times. The time-dependence of the $FAF$ reveals memory effects, which
increases as pc increases. The observed non-Markovian effects emerge due to the
interplay of cell division and mechanical feedback, and is inherently a
non-equilibrium phenomenon.
