The assumptions made here are not time reversible as the macrostate at time t+1 being deterministic given the macrostate at time t, does not imply that the macrostate at time t is deterministic given the macrostate at time t+1.
So in this article the direction of time is given through the asymmetry of the evolution of macrostates.
Yup. Also, I’d add that entropy in this formulation increases exactly when more than one macrostate at time t maps to the same actually-realized macrostate at time t+1, i.e. when the macrostate evolution is not time-reversible.
The assumptions made here are not time reversible as the macrostate at time t+1 being deterministic given the macrostate at time t, does not imply that the macrostate at time t is deterministic given the macrostate at time t+1.
So in this article the direction of time is given through the asymmetry of the evolution of macrostates.
Yup. Also, I’d add that entropy in this formulation increases exactly when more than one macrostate at time t maps to the same actually-realized macrostate at time t+1, i.e. when the macrostate evolution is not time-reversible.