Entropy generation in cosmological particle creation and interactions: A statistical subdynamics analysis

This paper applies a statistical-mechanics notion of nonequilibrium entropy to a quantum field in a cosmological setting. The key idea is to view the bosonic field as a collection of harmonic oscillators, with natural frequencies Ω(t), and to define a time-dependent entropy S(t) which reflects correlations among the oscillators. The S so defined will be a constant of the motion in the absence of couplings, so that, e.g., there can be no entropy generation for a source-free linear field in a conformally static spacetime. If, however, interactions are induced by nonlinearities, material sources, or a more general dynamical background, S will exhibit a nontrivial time dependence. The form of this time dependence can be analyzed through the introduction of a ‘‘subdynamics,’’ and one concludes that, at least in one limit, dS/dt>0. Specifically, in addition to the ‘‘stimulated’’ changes in entropy, which reflect the choice of initial conditions and which can be either negative or positive, there will also be a ‘‘spontaneous’’ change in S induced by the dynamics which, at least for short times, is necessarily positive. The subdynamics analysis can also be applied to the phenomenon of particle creation, and one concludes that, here as well, there is a ‘‘natural’’ decomposition into a ‘‘spontaneous’’ particle creation induced by the dynamics, which leads to the net generation of quanta and a ‘‘simulated’’ change in particle number reflecting the choice of initial conditions, which is of indeterminate sign. The ‘‘spontaneous’’ contributions to particle creation can in turn be decomposed into two positive contributions: one, reflecting the effects of correlations, which is connected with spontaneous entropy generation, and another, induced by the time dependence of the Ω’s, which reflects instead a type of ‘‘phase mixing.’’