Both the first and the second derivatives of the chemical potential with respect to the temperature, for any system of noninteracting bosons, are shown to be negative. For noninteracting fermions, these derivatives can be either negative or positive, but for generic spectra they are both negative at higher temperatures.

中文翻译：

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非相互作用粒子的化学势的一阶和二阶导数

对于任何非相互作用玻色子系统，化学势相对于温度的一阶和二阶导数都显示为负值。对于非相互作用费米子，这些导数可以是负的也可以是正的，但对于一般光谱，它们在较高温度下都是负的。