Relaxation Dynamics and Finite-Size Effects in a Simple Model of Condensation

In this paper, 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 > 2a2: in the localized phase a single site hosts a ¯nite fraction of the whole energy. Its equilibrium properties in the thermodynamic limit are known and in a recent paper [G. Gotti, S. Iubini and P. Politi, Finite-size localization scenarios in condensation transitions, Phys. Rev. E 103 (2021) 052133] we studied the transition for ¯nite systems. Here, we analyze ¯nite-size e®ects 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