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Thomas,
Energy, being conserved, moves from one form to another. Since energy is conserved, in order for new forms to come into being, old forms have to dissolve. The past to future is energy moving on. The future to past is the forms being created and dissolved. Time is what a clock measures. We think of a clock as hands and face. Hands represent the present and the face is the events/units. To the events, the present seems to move, but to the present, it is the events which move the other way. To the hands, the face goes counterclockwise. This is much as we see the sun going east to west and finally realized it was the earth moving west to east.
Yes, it is future to present to past. That's the problem with the Schrodinger's cat paradox.It isn't movement along a time vector from past to future, but the actual events happening, deciding what the fate of the cat is. Think in terms of a race. Prior to the race, there are many potential winners, but then the race is run and there is only one actual winner.
The situation with entropy is that energy naturally expands, while mass contracts, so when released from mass, energy expands out in all directions very rapidly, but mass only consolidates out of energy very slowly, so the opposite effects do not mirror each other. The teacup doesn't reassemble itself. I think we will eventually realize mass is not so much a property of mass, but an effect of energy turning into mass and creating a vacuum. Much as when mass turns into energy, it creates pressure, like an explosion. They can't find dark energy, but galaxies are surrounded by fields of cosmic rays. If this energy is condensing into interstellar gasses, it would contract, creating a vacuum effect. Stars and large planets are constantly turning lighter forms of mass into denser forms of mass and these would explain their gravity fields.
Late for work....