繁星客栈 - 观星楼 (自然科学论坛)

HPC

发表文章数: 244
武功等级: 逍遥拳
　　　　　(第七重)
内力值: 206/206

相对论性的统计物理

咱们通常所学的maxwell 速度分布率，现在看来是违背光速原理的，以前尽然没有注意这一点，经常听人说，统计热力学与狭义相对论有些矛盾，但一直不是很理解。其中一个似乎很著名的问题就是，在静止参考系所看到的温度和运动参考系看到的温度孰高孰低似乎都没有定论。
不知各位大侠对此怎么看。

Faith, Fashion and Fancy.

Welcome to 我的域名：http://hongbaozhang.blog.edu.cn

发表时间：2005-10-08, 20:42:18

作者资料

权权

发表文章数: 92
武功等级: 罗汉拳
　　　　　(第一重)
内力值: 145/145

Re: 相对论性的统计物理

(1) The first princeple of statistical mechanics relies on Liouville theorem, ergodic assumption or uniform probability distribution in the energy shell in phase space. These statements are results of canonical theory and have the same form in relativistic case as in non-relativistic case. Partition function can still be written as configurational integral over phase space, with the relativistic Hamiltonian on the exponents.

For non-relativistic ideal gas, the configurational integral over momentum finnally reduced to simple Gauss integral. Using the relativistic relation of energy and momentum instead, this configurational integral also has analytical expression, expressed in terms of Hankel function of the second kind, and in high temperature limit has the asymptotic behavior of non-relativistic gas.

In treating ideal quantum gas, the typical way in text book is also substituting the relativistic Hamiltonian into the expression of partiton function. A famous example is black body radiation, regarding the radiation field as ultrarelativistic bosons.

(2) Another aspect of the question is the lorentz transformation of thermodynamic quantities. Let me think about it...

不忧不惧

发表时间：2005-10-09, 16:54:08

作者资料

孙伊