Abstract The induction time and metastable zone width (MSZW) measured for small samples (say 1 mL or less) both scatter widely. Thus, these two are observed as stochastic quantities. Whereas, for large samples (say 1000 mL or more), the induction time and MSZW are observed as deterministic quantities. The reason for such experimental differences is investigated with Monte Carlo simulation. In the simulation, the time (under isothermal condition) and supercooling (under polythermal condition) at which a first single crystal is detected are defined as the induction time t and the MSZW ΔT for small samples, respectively. The number of crystals just at the moment of t and ΔT is unity. A first crystal emerges at random due to the intrinsic nature of nucleation, accordingly t and ΔT become stochastic. For large samples, the time and supercooling at which the number density of crystals N/V reaches a detector sensitivity (N/V)det are defined as t and ΔT for isothermal and polythermal conditions, respectively. The points of t and ΔT are those of which a large number of crystals have accumulated. Consequently, t and ΔT become deterministic according to the law of large numbers. Whether t and ΔT may stochastic or deterministic in actual experiments should not be attributed to change in nucleation mechanisms in molecular level. It could be just a problem caused by differences in the experimental definition of t and ΔT.

中文翻译：

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诱导时间和亚稳区宽度的蒙特卡罗模拟；随机的还是确定的？

摘要 小样本（例如 1 mL 或更少）的诱导时间和亚稳区宽度 (MSZW) 测量值都分布广泛。因此，这两个被观察为随机量。而对于大样本（比如 1000 mL 或更多），诱导时间和 MSZW 被视为确定性数量。使用蒙特卡罗模拟研究了这种实验差异的原因。在模拟中，检测到第一个单晶的时间（在等温条件下）和过冷（在多温条件下）分别定义为小样品的诱导时间 t 和 MSZW ΔT。t 时刻与 ΔT 时刻的晶体数为 1。由于成核的内在性质，第一个晶体随机出现，因此 t 和 ΔT 变得随机。对于大样本，晶体数量密度 N/V 达到探测器灵敏度 (N/V)det 的时间和过冷度分别定义为等温和多温条件下的 t 和 ΔT。t点和ΔT点是大量结晶堆积的点。因此，根据大数定律，t 和 ΔT 成为确定性的。t 和 ΔT 在实际实验中是随机的还是确定性的，不应归因于分子水平上成核机制的变化。这可能只是由 t 和 ΔT 的实验定义差异引起的问题。因此，根据大数定律，t 和 ΔT 成为确定性的。t 和 ΔT 在实际实验中是随机的还是确定性的，不应归因于分子水平上成核机制的变化。这可能只是由 t 和 ΔT 的实验定义差异引起的问题。因此，根据大数定律，t 和 ΔT 成为确定性的。t 和 ΔT 在实际实验中是随机的还是确定性的，不应归因于分子水平上成核机制的变化。这可能只是由 t 和 ΔT 的实验定义差异引起的问题。