麦克斯韦-玻耳兹曼统计分布律的相对论修正

Relativistic modification on the Maxwell-Boltzmann statistical distribution formula

为了避免光速极限带来的复杂性,首先给出了理想气体分子动量的分布律公式.在此基础上,进一步讨论了麦克斯韦-玻耳兹曼统计分布律的相对论修正.解析和数值计算均表明,这一修正几乎没有可观测的物理效应.这说明,大学物理教学中介绍的麦克斯韦-玻耳兹曼速度分布律公式对实际应用已经足够精确.当然,我们决不可据此近似公式断言气体分子有一定的概率可以超光速运动.

To avoid the complication arising from the relativistic limitation of speed, at first, the momentum distribution formula of ideal gases is presented instead of speed. Then the relativistic modification on the Maxwell-Boltzmann distribution laws of speed is discussed. Analytic and numerical simulations show that this kind of modification has no observable effect. In other words, the Maxwell-Boltzmann distribution laws studied in university physics are good enough to describe the practical situations. However we cannot make a conclusion, based on these approximate formula, that molecules of ideal gas can move faster than the speed of light in vacuum.