I don’t think your graph is accurate. In our universe, entropy can reverse, but it’s unlikely, and an entropy reversal large enough to take us from heat-death to the current state of the universe is unimaginably unlikely. Given an infinite amount of time, that will eventually happen, but your graph should be entropy spikes surrounded by eternities at minimum entropy. Given that more-accurate graph, the probability that we’re in a decreasing-entropy part of the graph is ~100%.
Entropy “reversal”—i.e. decrease—must be equally frequent as entropy increases: you cannot have an increase if you didn’t have a decrease before. My graph is not quantitatively accurate for sure but with a rescaling of times it should be ok.
Sorry I got the terminology backwards. Entropy generally increases, so your graph should be mostly at maximum entropy with very short (at this timescale) downward spikes to lower entropy states.
It’s true that for entropy to increase you can’t already be at the maximum entropy state, but I’m not saying it constantly increases, I’m saying it increases until it hits maximum entropy and then stays near there unless something extraordinarily unlikely happens (a major entropy reversal).
I think the only scale where your graph works is if we’re looking at near-max-entropy for the entire time, which is nothing like the current state of the universe.
In the equilibrium, small increases and small decreases should be equally likely, with an unimaginably low probability of high decreases (which becomes 0 if the universe is infinite).
Yes, but our universe is not in equilibrium or anywhere near equilibrium. We’re in a very low entropy state right now and the state which is in equilibrium is extremely high entropy.
It’s actually worse than that. If you define Entropy using information theory, there is no such thing as random fluctuations decreasing Entropy. The system merely moves from one maximal Entropy state to the next, indefinitely.
I don’t think your graph is accurate. In our universe, entropy can reverse, but it’s unlikely, and an entropy reversal large enough to take us from heat-death to the current state of the universe is unimaginably unlikely. Given an infinite amount of time, that will eventually happen, but your graph should be entropy spikes surrounded by eternities at minimum entropy. Given that more-accurate graph, the probability that we’re in a decreasing-entropy part of the graph is ~100%.
Entropy “reversal”—i.e. decrease—must be equally frequent as entropy increases: you cannot have an increase if you didn’t have a decrease before. My graph is not quantitatively accurate for sure but with a rescaling of times it should be ok.
Sorry I got the terminology backwards. Entropy generally increases, so your graph should be mostly at maximum entropy with very short (at this timescale) downward spikes to lower entropy states.
It’s true that for entropy to increase you can’t already be at the maximum entropy state, but I’m not saying it constantly increases, I’m saying it increases until it hits maximum entropy and then stays near there unless something extraordinarily unlikely happens (a major entropy reversal).
I think the only scale where your graph works is if we’re looking at near-max-entropy for the entire time, which is nothing like the current state of the universe.
In the equilibrium, small increases and small decreases should be equally likely, with an unimaginably low probability of high decreases (which becomes 0 if the universe is infinite).
Yes, but our universe is not in equilibrium or anywhere near equilibrium. We’re in a very low entropy state right now and the state which is in equilibrium is extremely high entropy.
I agree—but, if understood correctly the OP, he is averaging over a time scale much larger than the time required to reach the equilibrium.
It’s actually worse than that. If you define Entropy using information theory, there is no such thing as random fluctuations decreasing Entropy. The system merely moves from one maximal Entropy state to the next, indefinitely.
If you work under the hypothesis that information is preserved, then the total entropy of the universe does not increase nor decrease.