In Landau and Lifshitz's Stat Mech Volume I is the comment:
Thus in quantum mechanics there is a physical non-equivalence of the two diretions of time, and theoretically the law of increase of entropy might be its macroscopic expression. In that case, there must exist an inequality involving the quantum constant $\hbar$ which ensures the validity of this law and is satisfied in the real world. Up to the present, however, no such relation has been at all convincingly shown to exist.
Has there been such convincing work relating the direction of time and $\hbar$ since these comments were first made (somewhere between 1937 and 1975 by the dates in the prefaces).