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 $h>2a^2$: 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 [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 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.

在本文中，我们考虑一个简单的纯随机模型，其特征在于两个守恒量（质量密度a和能量密度h），已知当$H>2A^2$：在局部阶段，单个位点承载着整个能量的有限部分。它在热力学极限下的平衡特性是已知的，并且在最近的一篇论文中 [G. Gotti、S. Iubini 和 P. Politi，凝结转变中的有限尺寸局部化场景，物理学。Rev. E  103 (2021) 052133]我们研究了有限系统的转变。在这里，我们分析了能量分布和弛豫动力学的有限尺寸效应，表明应该研究极大的系统以观察渐近分布，甚至应该模拟更大的系统以观察预期的弛豫动力学。