Hamiltonian Based nRules, Time's Arrow
  The auxiliary rules of quantum mechanics can be written without the Born rule by using what are called the nRules. The nRules are understood in part by making certain modifications in the Hamiltonian. In this paper, those modifications are written directly into the nRules, reducing their number from four to three. It is shown that the nRules in either form provide for a definite direction in time, guaranteeing that a statistically irreversible interaction is absolutely irreversible. 
Richard A Mould