用平均值法与最概然法推导粒子数分布不相等的一个实例

An Example Illustrating That Particle Number Distribution Deriving from the Mean Method Is Different from That Deriving from the Most Probable Method

在统计物理中,通常认为平均值等于最概然值,对近独立子系(如:非定域玻耳兹曼粒子系统、玻色子系统、费米子系统)粒子数分布的推导可佐证此结论.然而,研究发现:用平均值法与最概然法推导的定域玻耳兹曼粒子数分布的结果不同,两者相差N倍,而N为系统的粒子数,且通常N是很大的量.

In statistical physics, the mean value is generally believed to be equal to the most probable value. For near-independent subsystems (e.g. non-localized Boltzmann particle system, Bose subsystem, Fermi subsystem), the derivation of the particle number distribution can support this conclusion. However, we find that the result of the localized Boltzmann particle number deriving from the mean method is different from that deriving from the most probable method. The difference between them is N times. N is the number of particles of the system and is usually a large quantity.