Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probability distribution for the relative velocity of colliding
  particles in a relativistic classical gas   We find the probability density function $\mathcal{P}(V_{\texttt{r}})$ of the
relativistic relative velocity for two colliding particles in a non-degenerate
relativistic gas. The distribution reduces to Maxwell distribution for the
relative velocity in the non-relativistic limit. We find an exact formula for
the mean value $\langle V_{\texttt{r}}\rangle$. The mean velocity tends to the
Maxwell's value in the non-relativistic limit and to the velocity of light in
the ultra-relativistic limit. At a given temperature $T$, when at least for one
of the two particles the ratio of the rest energy over the thermal energy $m
c^2/k_B T$ is smaller than 40 the Maxwell distribution is inadequate.

13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
18
The categories of this paper are: econ