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.
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.Abstract. The arrow-of-time dilemma states that the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e., entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.