Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-equilibrium Quantum Many-Body Green Function Formalism in the light
  of Quantum Information Theory   The following issues are discussed inspired by the recent paper of Kadanoff
(arXiv: 1403:6162): (a) Construction of a generalized one-particle Wigner
distribution (GWD) function (analog of the classical distribution function)
from which the quantum kinetic equation due to Kadanoff and Baym (KB) is
derived, often called the Quantum Boltzmann Equation (QBE); (b) The equation
obeyed by this has a collision contribution in the form of a two-particle Green
function. This term is manipulated to have Kinetic Entropy in parallel to its
counterpart in the classical Boltzmann kinetic equation for the classical
distribution function. This proved to be problematic in that unlike in the
classical Boltzmann kinetic equation, the contribution from the kinetic entropy
term was non-positive; (3) Kadanoff surmised that this situation could perhaps
be related to quantum entanglement that may not have been included in his
theory. It is shown that GWD is not positive everywhere (indicating dynamical
quantumness) just like the commonly recognized property of the Wigner function
(negative property indicating quantumness of the state). The issue of
non-positive feature appearing in approximate evaluation of patently positive
entities in many particle systems is here pointed to an early discussion of
this issue (Phys. Rev. A10, 1852 (1974)) in terms of a theorem on truncation of
cumulant expansion of a probability distribution function due to Marcinkeiwicz.
The last issue of presence or absence of entanglement in an approximate
evaluation of a many particle correlation poses a new problem; it is considered
here in terms of fermionic entanglement theory in the light of density matrix
and Green function theory of many-fermion systems. The clue comes from the fact
that the Hartree-Fock approximation exhbits no entantanglement in two-particle
fermion density matrix and hence also in two-particle Green function.

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The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph