最大熵原理导出理想气体分子的速度和速率分布

最大熵原理是统计物理的一个基本原理,它已在很多领域得到广泛应用。使用最大熵原理分别研究了平衡态下,三维、二维和一维理想气体分子的速度分布,导出了它们的速度分布概率密度函数,并进而得到了速率分布的概率密度函数。这一方面给出了推导理想气体分子速度和速率分布规律的另一方法,另一方面也拓展了最大熵原理的应用范围。

Using Maximum Entropy Principle to Deduce the Velocity Distribution of Ideal Gas Molecules

The maximum entropy principle is a basic law of statistical physics, and it has been widely used in various fields. The paper uses the maximum entropy principle to study the velocity distributions of three-dimensional, two-dimensional and one-dimensional ideal gas molecules in the equilibrium state, respectively. The probability density functions of velocity are deduced, and then the probability density functions of rate are deduced, too. This provides an alternative approach to deduce the velocity distribution of ideal gas molecules; on the other hand, it also extends the range of applications of maximum entropy principle.