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The following issues are discussed inspired by the recent paper of Kadanoff(arXiv: 1403:6162): (a) Construction of a generalized one-particle Wignerdistribution (GWD) function (analog of the classical distribution function)from which the quantum kinetic equation due to Kadanoff and Baym (KB) isderived, often called the Quantum Boltzmann Equation (QBE); (b) The equationobeyed by this has a collision contribution in the form of a two-particle Greenfunction. This term is manipulated to have Kinetic Entropy in parallel to itscounterpart in the classical Boltzmann kinetic equation for the classicaldistribution function. This proved to be problematic in that unlike in theclassical Boltzmann kinetic equation, the contribution from the kinetic entropyterm was non-positive; (3) Kadanoff surmised that this situation could perhapsbe related to quantum entanglement that may not have been included in histheory. It is shown that GWD is not positive everywhere (indicating dynamicalquantumness) just like the commonly recognized property of the Wigner function(negative property indicating quantumness of the state). The issue ofnon-positive feature appearing in approximate evaluation of patently positiveentities in many particle systems is here pointed to an early discussion ofthis issue (Phys. Rev. A10, 1852 (1974)) in terms of a theorem on truncation ofcumulant expansion of a probability distribution function due to Marcinkeiwicz.The last issue of presence or absence of entanglement in an approximateevaluation of a many particle correlation poses a new problem; it is consideredhere in terms of fermionic entanglement theory in the light of density matrixand Green function theory of many-fermion systems. The clue comes from the factthat the Hartree-Fock approximation exhbits no entantanglement in two-particlefermion density matrix and hence also in two-particle Green function.

Non-equilibrium Quantum Many-Body Green Function Formalism in the light of Quantum Information Theory