There have been a proposed solution to the Quantum vs Thermodynamic arrow of time problem published in the Phys. Rev. Letters. If my understanding is correct, the idea is very simple - time flows symmetrically in both directions, but observers only can remember the forward flow. http://link.aps.org/doi/10.1103/PhysRevLett.103.080401 http://arxiv.org/abs/0802.0438 It sounds reasonable, but wouldn't it break unitarity (at least in a subjective observer view)? It also seems to me that it would bias the wave function collapse - an elementary outcome which leave a "larger trail of information behind" would be more likely to be observed.