I am puzzled with thought experiment that resembles/is version of Bolzmann's brain-hyphothesis. I could explain it in following way:
Let’s assume that we have isolated system full of some stuff, let’s say room full of air. We have some entropy meter in that room and we can also observe what happens in the room.
As well known, air particles in room are bumping on each other. Sometimes, very very rarely, all particles might be packed in the other half of the room and other half would be empty. On that time instant, entropy in room decreases rapidly and there is some usable energy in the room. Let’s take a leap of faith and assume that on that instant life would pop up in that room.
Here comes the catch that confuses me: Direction of time is always thought to be pointing towards state of higher entropy. Then, if life would pop up on downward slope of measured entropy curve (when entropy starts to drop), life inside the room would assume that arrow of time is opposite than ours (Direction to higher entropy inside the room is opposite to our arrow of time). If life would pop up on upward slope of measured entropy curve, life inside the room would have same direction of time than we would.
Am I missing something here? It seems counter intuitive that time in some insulated system at times might have different direction than system surrounding it.
It's getting even more confusing when trying to think how speed of time in such room would compare to ours. Maybe speed of time in that room would be somewhat relational to slope? If slope is steep, maybe time for beings in the room would be fast?