Hartle, James B.
A model quantum cosmology is used to illustrate how arrows of time emerge in a universe governed by a time-neutral dynamical theory (H) constrained by time asymmetric initial and final boundary conditions represented by density matrices ρI and ρF . In a quantum universe universe arrows of time are described by the probabilities of appropriately coarse grained sets of histories of quantities like entropy that grow or decay. We show that the requirement of that these sets of histories decohere implies two things: (1) A time asymmetry between initial and final conditions that is a basis for arrows ot time. (2) How a final state of indifference that is represented by a density matrix ρF proportional to the unit density matrix is consistent with causality, and allows a finer-grained description of the model universe in terms of decoherent histories than any other final state.