Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vlasov equation and $N$-body dynamics - How central is particle dynamics
  to our understanding of plasmas?   Difficulties in founding microscopically the Vlasov equation for
Coulomb-interacting particles are recalled for both the statistical approach
(BBGKY hierarchy and Liouville equation on phase space) and the dynamical
approach (single empirical measure on one-particle
$(\mathbf{r},\mathbf{v})$-space). The role of particle trajectories
(characteristics) in the analysis of the partial differential Vlasov--Poisson
system is stressed. Starting from many-body dynamics, a direct derivation of
both Debye shielding and collective behaviour is sketched.

19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con