Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statics and dynamics of inhomogeneous liquids via the internal-energy
  functional   We give a variational formulation of classical statistical mechanics where
the one-body density and the local entropy distribution constitute the trial
fields. Using Levy's constrained search method it is shown that the grand
potential is a functional of both distributions, that it is minimal in
equilibrium, and that the minimizing fields are those at equilibrium. The
functional splits into a sum of entropic, external energetic and internal
energetic contributions. Several common approximate Helmholtz free energy
density functionals, such as the Rosenfeld fundamental measure theory for hard
sphere mixtures, are transformed to internal energy functionals. The
variational derivatives of the internal energy functional are used to
generalize dynamical density functional theory to include the dynamics of the
microscopic entropy distribution, as is relevant for studying heat transport
and thermal diffusion.

7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn