Entropy, quantum decoherence and pointer states scalar “parton” fields

Entropy arises in strong interactions by a dynamical separation of “partons” from long-wavelength “environment” modes due to confinement. We evaluate the time dependent von Neumann entropy for a general model of two interacting scalar fields representing, for example, partons and their environment, respectively. The relevant density functional is diagonalized in time-dependent Hartree-Fock approximation based on the functional Schrödinger picture. This yields “field pointer states” and their probabilities in terms of Wightman functions. Our approach can be applied to a variety of related non-equilibrium problems. The results also indicate how to calculate a finite geometric entropy proportional to a surface area.