Damped Perturbations in the No-Boundary State.

We evaluate the no-boundary path integral exactly in a Bianchi type IX minisuperspace with two scale factors. In this model the no-boundary proposal can be implemented by requiring one scale factor to be zero initially together with a judiciously chosen regularity condition on the momentum conjugate to the second scale factor. Taking into account the nonlinear backreaction of the perturbations we recover the predictions of the original semiclassical no-boundary proposal. In particular we find that large perturbations are strongly damped, consistent with vacuum state wave functions.

Entropy of classical histories.

We consider a number of proposals for the entropy of sets of classical coarse-grained histories based on the procedures of Jaynes, and we prove a series of inequalities relating these measures. We then examine these as a function of the coarse-graining for various classical systems, and show explicitly that the entropy is minimized by the finest-grained description of a set of histories. We propose an extension of the second law of thermodynamics to the entropy of histories. We briefly discuss the implications for decoherent or consistent history formulations of quantum mechanics.