Expanding on the billiard ball example: lets say one part of the wall of the pool table adds some noise to the trajectory of the balls that bounce off of that spot, but doesn’t sap energy from them on average. After a while we won’t know the exact positions of the balls at an arbitrary time given only their initial positions and momenta. That is, entropy has entered our system through that part of the wall. I know this language makes it sound like entropy is in the system, flowing about, but if we knew the exact shape of the wall at that spot then it wouldn’t happen.
Even with this entropy entering our system, the energy remains constant. This is why total energy is a wonderful macrovariable for this system. Systems where this works are usually easily solved as a microcanonical ensemble. If, instead, that wall spot was at a fixed temperature, we would use the canonical ensemble.
Expanding on the billiard ball example: lets say one part of the wall of the pool table adds some noise to the trajectory of the balls that bounce off of that spot, but doesn’t sap energy from them on average. After a while we won’t know the exact positions of the balls at an arbitrary time given only their initial positions and momenta. That is, entropy has entered our system through that part of the wall. I know this language makes it sound like entropy is in the system, flowing about, but if we knew the exact shape of the wall at that spot then it wouldn’t happen.
Even with this entropy entering our system, the energy remains constant. This is why total energy is a wonderful macrovariable for this system. Systems where this works are usually easily solved as a microcanonical ensemble. If, instead, that wall spot was at a fixed temperature, we would use the canonical ensemble.