Relaxation dynamics and finite-size effects in a simple model of condensation

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.