If you don’t know anything about what’s gonna happen to x it’s more likely that it will transfer to a macrostate with a higher number of representatives than to one with a low number of representatives.
Does this explain time-asymmetry? Well, let’s check the time-reverse of your sentence.
If you don’t know anything about what happened to x it’s more likely that it transferred from a macrostate with a higher number of representatives than f rom one with a low number of representatives.
Hmm… This sentence seems just as plausible, but it implies that entropy increases into the past.
But clearly entropy does increase, so how do we explain it?
Well, if the dynamics are time-symmetric, and the boundary conditions are time-symmetric, then the behaviour of the system is also time-symmetric. (Symmetry in, symmetry out!) Therefore, if the behaviour of the system is time-asymmetric, and the dynamics are time-symmetric, then the boundary conditions must be time-asymmetric.
In other words, at one boundary of space-time, the universe is low-entropy, and at the other boundary of space-time, the universe is high-entropy. For convenience, we call the low-entropy boundary the “start” and the high-entropy boundary the “end”. And we say one event is “earlier” than another if and only if it occurs closer to the low-entropy boundary.
This argument does not work!
Does this explain time-asymmetry? Well, let’s check the time-reverse of your sentence.
Hmm… This sentence seems just as plausible, but it implies that entropy increases into the past.
This is called Loschmidt’s Paradox. You can read about it here.
But clearly entropy does increase, so how do we explain it?
Well, if the dynamics are time-symmetric, and the boundary conditions are time-symmetric, then the behaviour of the system is also time-symmetric. (Symmetry in, symmetry out!) Therefore, if the behaviour of the system is time-asymmetric, and the dynamics are time-symmetric, then the boundary conditions must be time-asymmetric.
In other words, at one boundary of space-time, the universe is low-entropy, and at the other boundary of space-time, the universe is high-entropy. For convenience, we call the low-entropy boundary the “start” and the high-entropy boundary the “end”. And we say one event is “earlier” than another if and only if it occurs closer to the low-entropy boundary.