Dipartimento di Fisica, Università di Roma Sapienza, P. le Aldo Moro 2, 00185 Rome, Italy.
Phys Rev E. 2018 Jul;98(1-1):012121. doi: 10.1103/PhysRevE.98.012121.
In systems with long-range interactions, since energy is a nonadditive quantity, ensemble inequivalence can arise: it is possible that different statistical ensembles lead to different equilibrium descriptions, even in the thermodynamic limit. The microcanonical ensemble should be considered the physically correct equilibrium distribution as long as the system is isolated. The canonical ensemble, on the other hand, can always be defined mathematically, but it is quite natural to wonder to which physical situations it does correspond. We show numerically and, in some cases, analytically that the equilibrium properties of a generalized Hamiltonian mean-field model in which ensemble inequivalence is present are correctly described by the canonical distribution in (at least) two different scenarios: (a) when the system is coupled via local interactions to a large reservoir (even if the reservoir shows, in turn, ensemble inequivalence), and (b) when the mean-field interaction between a small part of a system and the rest of it is weakened by some kind of screening.
在具有长程相互作用的系统中，由于能量不是可加的量，因此可能会出现系综不等价：即使在热力学极限下，不同的统计系综也可能导致不同的平衡描述。只要系统是孤立的，正则系综应该被认为是物理上正确的平衡分布。另一方面，正则系综在数学上总是可以定义，但很自然地会想知道它对应于哪些物理情况。我们通过数值和在某些情况下的分析表明，在存在系综不等价的广义哈密顿平均场模型中，平衡性质可以通过正则分布来正确描述（至少在两种不同的情况下）：（a）当系统通过局部相互作用与大的储库耦合时（即使储库本身也显示出系综不等价），以及（b）当系统的一小部分与其余部分之间的平均场相互作用被某种屏蔽削弱时。
