Correlation entropy of an interacting quantum field andHtheorem for theO(N)model

Abstract

Following the paradigm of Boltzmann-BBGKY we propose a correlation entropy (of the nth order) for an interacting quantum field, obtained by 'slaving' (truncation with causal factorization) of the higher (n+1 th) order correlation functions in the Schwinger-Dyson system of equations. This renders an otherwise closed system effectively open where dissipation arises. The concept of correlation entropy is useful for addressing issues related to thermalization. As a small yet important step in that direction we prove an H-theorem for the correlation entropy of a quantum mechanical O(N) model with a Closed Time Path Two Particle Irreducible Effective Action at the level of Next-to-Leading-Order large N approximation. This model may be regarded as a field theory in 0 space dimensions.

Quantum kinetic theory of a Bose-Einstein gas confined in a lattice

“…We describe the conceptual pathway for the construction of quantum kinetic theory from the nPI effective action. Though somewhat theoretical and formally oriented, it may be of some use, as this is the first point of contact with quantum kinetic theory from the effective action approach, in the atomic and molecular physics (AMO) context(For more details on this subject see [19,20,21,22], where our discussions in the following section are based on).…”

“…The situation in quantum kinetic field theory is completely analogous. One may choose to work with a truncation of the hierarchy of the Wigner function and its higher correlation analogs, or one may instead perform a slaving of, for example, the Wigner-transformed four-point function, which leads (within the context of perturbation theory) directly to the (relativistic) Boltzmann equation [19] and the usual H-theorem [22]. Typically this slaving of the higher correlation function(s) involves imposing causal boundary conditions to obtain a particular solution for the higher correlation function(s) in terms of the lower order correlation functions [19,20].…”

Uniqueness of thermodynamic projector and kinetic basis of molecular individualism

“…Then the last term in Eqs. (38), (39) vanishes. It is the case of quasiequilibrium manifolds, for example [28,29].…”

“…(36), and the result was not a solution of this equation. Very recently the short memory approximation becomes more popular [37,38].…”

“…(36), (38), (39) has one free parameter: the memory time τ (Ψ). The next step is development of the theory without such free parameters [32,33].…”