While the canonical ensemble has been tremendously successful in capturing statistical properties of large systems, deviations from canonical behavior exhibited by small systems are not well understood. Here, using a two-dimensional small Ising magnet embedded inside a larger heat bath, we characterize the failures of the canonical ensemble when describing small systems. We find significant deviations from the canonical behavior for small systems near and below the critical point. Notably, the agreement with the canonical ensemble is driven not by the system size but by the decoupling between the system and its surrounding. A superstatistical framework wherein we allow the temperature of the small magnet to vary is able to capture the statistics of the small magnet with significantly higher accuracy than the Gibbs–Boltzmann distribution. We discuss implications for experiments and future directions.

尽管规范合奏在捕获大型系统的统计特性方面已取得巨大成功，但对小型系统所表现出的与规范行为的偏差却知之甚少。在这里，我们使用嵌入较大热浴池中的二维小型Ising磁体，描述了小型系统时，描述了典型系综的故障。对于临界点附近和之下的小型系统，我们发现其与规范行为存在显着偏差。值得注意的是，与规范合奏的协议不是由系统规模决定的，而是由系统与其周围环境之间的去耦关系决定的。我们允许小磁体的温度变化的超统计框架能够以比Gibbs–Boltzmann分布更高的精度捕获小磁体的统计信息。