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

TL;DR

This paper investigates how finite system size influences the energy distribution and relaxation dynamics in a simple stochastic model exhibiting a condensation transition, emphasizing the need for very large systems to observe asymptotic behaviors.

Contribution

It provides a detailed analysis of finite-size effects on energy distribution and relaxation dynamics in a condensation model, extending previous equilibrium studies.

Findings

Finite-size effects significantly alter energy distribution near the transition.

Very large systems are required to observe asymptotic distribution.

Even larger systems are needed to capture the true relaxation dynamics.

Abstract

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.