Research on fluctuations in energy and temperature is presented for a small specimen. The small specimen in contact with a heat bath shows energy fluctuations, ΔE, at the constant temperature. On the other hand, when this small specimen is isolated from the reservoir and adiabatic isolation is kept, it exhibits temperature fluctuations, ΔT, at the constant energy. This means that the temperature is unsharp if a sharp energy is assigned. A complementary relation between ΔE and ΔT is proposed in a simple formula. The connection between ΔE and ΔT is mediated by the heat capacity CV(T). This complementary relation is valid in general and it does not depend on the amount of substance. If the constituent numberN of the system is of the order of Avogadro’s number, then the fluctuations have been masked by large Nand we cannot see the influence of the fluctuations. However, when the number N decreases, the intrinsic features of fluctuations come out gradually. This paper presents the quantitative analyses of the fluctuations in the energy and temperature for several physical models. Typical characteristics in the fluctuations can be clearly seen only in a small specimen, which are shown in the graphical representations. It is stressed that the values of ΔE and ΔT are defined for the different prescribed conditions specified above.

中文翻译：

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小样本能量和温度波动的互补关系

针对一个小样本提出了关于能量和温度波动的研究。与热浴接触的小样本显示出能量波动，Δ乙, 在恒温下。另一方面，当这个小样本与水库隔离并保持绝热隔离时，它会表现出温度波动，Δ吨，在恒定能量下。这意味着如果分配了尖锐的能量，则温度不清晰。互补关系Δ乙和Δ吨以一个简单的公式提出。之间的联系Δ乙和Δ吨由热容量介导C五(吨). 这种互补关系一般是有效的，它不依赖于物质的数量。如果成分数ñ系统的数量级为阿伏伽德罗数，则波动已被大ñ我们看不到波动的影响。然而，当数ñ减少，波动的内在特征逐渐显现。本文介绍了几种物理模型的能量和温度波动的定量分析。波动的典型特征只能在小样本中清楚地看到，如图所示。强调的是价值观Δ乙和Δ吨是针对上述规定的不同规定条件而定义的。