Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modifications of the Ornstein-Zernike Relation and the LMBW Equations in
  the Canonical Ensemble via Hilbert-Space Methods   Application of the density functional formalism to the canonical ensemble is
of practical interest in cases where there is a marked difference between, say,
the canonical and the grand canonical ensemble (cavities or pores). An
important role is played by the necessary modification of the famous
Ornstein-Zernike relation between pair correlation and direct correlation
function, as the former is no longer invertible in a strict sense in (finite)
canonical ensembles. Here we approach the problem from a different direction
which may complement the density functional approach. In particular, we develop
rigorous canonical ensemble versions of the LMBW equations, relating density
gradient and exterior potential in the presence of explicit (singular)
containing potentials. This is accomplished with the help of integral operator
and Hilbert space methods, yielding among other things representations of the
direct correlation function on certain subspaces. The results are particularly
noteworthy and transparent if the segregating potential is a linear
(gravitational) one. In that case the modifications in the LMBW equations can
be expressed as pure, seemingly non-local integrations over the container
boundaries.

9
The categories of this paper are: nlin
19
The categories of this paper are: eess
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom