I find myself not quite satisfied with your argument about “why entropy (almost) always goes up”—it feels as if there’s some sleight of hand going on—but I’m not sure exactly where to locate my dissatisfaction. Let me try to express it...
First of all, although you use the word “stable” to describe the property of matter you’re appealing to, I don’t think that’s right. I think what you’re actually using is much more like “consistent” than “stable”. Consider a standard thought experiment. We have a sealed container with an impermeable partition half way across. We remove all the air from one half. Then we suddenly break or remove the partition, and of course the air pressure rapidly equalizes. The macrostate transition y → y’ is from “container with air at 1atm on the left and vacuum on the right” to “container with air at 0.5atm throughout”; y->y’ is a plausible thing and y’->y is not. But I don’t think this asymmetry has anything to do with stability; it’s not as if y->y’ is a smaller change than y’->y. Rather, the thing you need is that both y and y’ consistently almost always yield y’.
OK, so now we find that most macrostates have almost-perfectly-consistent successors, but less-consistent predecessors. (This is the time-asymmetry we need to get anything like the second law.) E.g., y’ is preceded by y much more often than it is followed by y, even though if we consider all microstates corresponding to y’ exactly the same fraction are preceded and followed by microstates corresponding to y.
Well, why is that? Isn’t it unexpected? It should be (at least if we’re considering what the laws of physics entail, rather than what we find in our everyday experience). So let’s ask: why do things behave more consistently “forwards” than “backwards”?. I think the answer, unfortunately, is: “Because of the second law of thermodynamics” or, kinda-equivalently, “Because the universe has a low-entropy past”.
Consider that partitioned container again. If we picked a present microstate truly at random from all those whose corresponding macrostate is “0.5atm air in the whole container”, the probability is vanishingly small that we’d find a microstate like the real one whose recent past has all the air collected into half of the container. So however did it come about that we do now have such a microstate? As a result of the lower-entropy past. How will it come about in the future that we find ourselves in such microstates? As a result of the low-entropy present, which will then be a lower-entropy past.
So it seems as if the “stability” (by which, again, I think you mean “consistency of behaviour”) of matter only explains the thermodynamic arrow of time if we’re allowed to assume a lower-entropy past. And if we can make that assumption, we can get the Second Law without needing to appeal explicitly to the consistent behaviour of matter.
(On the other hand, considered as a way of understanding how the low-entropy past of the universe leads to the Second Law, I think I like it.)
I find myself not quite satisfied with your argument about “why entropy (almost) always goes up”—it feels as if there’s some sleight of hand going on—but I’m not sure exactly where to locate my dissatisfaction. Let me try to express it...
First of all, although you use the word “stable” to describe the property of matter you’re appealing to, I don’t think that’s right. I think what you’re actually using is much more like “consistent” than “stable”. Consider a standard thought experiment. We have a sealed container with an impermeable partition half way across. We remove all the air from one half. Then we suddenly break or remove the partition, and of course the air pressure rapidly equalizes. The macrostate transition y → y’ is from “container with air at 1atm on the left and vacuum on the right” to “container with air at 0.5atm throughout”; y->y’ is a plausible thing and y’->y is not. But I don’t think this asymmetry has anything to do with stability; it’s not as if y->y’ is a smaller change than y’->y. Rather, the thing you need is that both y and y’ consistently almost always yield y’.
OK, so now we find that most macrostates have almost-perfectly-consistent successors, but less-consistent predecessors. (This is the time-asymmetry we need to get anything like the second law.) E.g., y’ is preceded by y much more often than it is followed by y, even though if we consider all microstates corresponding to y’ exactly the same fraction are preceded and followed by microstates corresponding to y.
Well, why is that? Isn’t it unexpected? It should be (at least if we’re considering what the laws of physics entail, rather than what we find in our everyday experience). So let’s ask: why do things behave more consistently “forwards” than “backwards”?. I think the answer, unfortunately, is: “Because of the second law of thermodynamics” or, kinda-equivalently, “Because the universe has a low-entropy past”.
Consider that partitioned container again. If we picked a present microstate truly at random from all those whose corresponding macrostate is “0.5atm air in the whole container”, the probability is vanishingly small that we’d find a microstate like the real one whose recent past has all the air collected into half of the container. So however did it come about that we do now have such a microstate? As a result of the lower-entropy past. How will it come about in the future that we find ourselves in such microstates? As a result of the low-entropy present, which will then be a lower-entropy past.
So it seems as if the “stability” (by which, again, I think you mean “consistency of behaviour”) of matter only explains the thermodynamic arrow of time if we’re allowed to assume a lower-entropy past. And if we can make that assumption, we can get the Second Law without needing to appeal explicitly to the consistent behaviour of matter.
(On the other hand, considered as a way of understanding how the low-entropy past of the universe leads to the Second Law, I think I like it.)