理想体系巨正则系综中粒子数密度的热力学涨落

Thermodynamical Fluctuation of Number Density of Particles in Grand Canonical Ensemble of Perfect Systems

巨正则系综与大粒子源相接触，它的化学势是一个常数，而系统的粒子数可以涨落．对体积 一定的系统，密度与粒子数成正比，用巨正则系综求解热力学系统的粒子数和密度的涨落是可行 的．由巨正则系综的配分函数，结合热力学关系，首先将粒子数密度的涨落用易观测的量表示出 来，然后由低温和高温体系的状态方程，通过严格的理论推导，给出理想体系在低温和高温情况下 的粒子数密度的热力学涨落规律，并对其进行物理分析．

The chemistry potential of grand canonical ensemble contacting big particle fountain is a con- stant. The particle numbers of system may fluctuate. For the system of definite volume, density be- ing directly proportional to particle number, solving the fluctuation of particle numbers and density of thermodynamical system is viable by using grand canonica1 ensemble. At first the fluctuation of num- ber density of particles is expressed into easy observation quantum by partition function of grand canonical ensemble and linking thermodynamical relation. Then through state equation of system un- der low temperature conditions,thermodynamical low for fluctuation in number density of particles of perfect system is given under low and high temperature conditions. lt is physically analyzed.