  We consider a simple, purely stochastic model characterized by two conserved
quantities (mass density $a$ and energy density $h$) which is known to display
a condensation transition when $h > 2a^2$: in the localized phase a single site
hosts a finite fraction of the whole energy. Its equilibrium properties in the
thermodynamic limit are known and in a recent paper (Gabriele Gotti, Stefano
Iubini, Paolo Politi, Phys. Rev. E 103, 052133 (2021)) we studied the
transition for finite systems. Here we analyze finite-size effects on the
energy distribution and on the relaxation dynamics, showing that extremely
large systems should be studied in order to observe the asymptotic distribution
and even larger systems should be simulated in order to observe the expected
relaxation dynamics.
