# Entropy Decreases?

I've always been slightly confused by the Second Law of Thermo. For example, with Maxwell's Demon, where a demon controls the partition between two gas chambers to select all the fast moving particles into one chamber, the Second Law is not violated because the demon's actions and thought process increases entropy. However, say that the demon was removed. By pure random chance, isn't it entirely possible that the fast, hot particles will move into one chamber and the cold, slow particles will move into the other chamber? All textbooks/guides/videos say that yes, it is possible, but the chances are extremely small. Thus, when this situation actually happens after a very long time, entropy decreases, so isn't this a direct violation of the Second Law of Thermo? Assuming that the system is in an isolated vacuum, this also means that there can be no transfer of heat to the surroundings, so there is nothing else that can gain entropy. How is my thought process incorrect? Thanks!

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stevendaryl
Staff Emeritus
I've always been slightly confused by the Second Law of Thermo. For example, with Maxwell's Demon, where a demon controls the partition between two gas chambers to select all the fast moving particles into one chamber, the Second Law is not violated because the demon's actions and thought process increases entropy. However, say that the demon was removed. By pure random chance, isn't it entirely possible that the fast, hot particles will move into one chamber and the cold, slow particles will move into the other chamber? All textbooks/guides/videos say that yes, it is possible, but the chances are extremely small. Thus, when this situation actually happens after a very long time, entropy decreases, so isn't this a direct violation of the Second Law of Thermo? Assuming that the system is in an isolated vacuum, this also means that there can be no transfer of heat to the surroundings, so there is nothing else that can gain entropy. How is my thought process incorrect? Thanks!
The second law is considered by most physicists to be a statistical. It is not impossible for entropy to decrease, but it is overwhelmingly likely, for large systems.

Andrew Mason
Homework Helper
I've always been slightly confused by the Second Law of Thermo. For example, with Maxwell's Demon, where a demon controls the partition between two gas chambers to select all the fast moving particles into one chamber, the Second Law is not violated because the demon's actions and thought process increases entropy. However, say that the demon was removed. By pure random chance, isn't it entirely possible that the fast, hot particles will move into one chamber and the cold, slow particles will move into the other chamber? All textbooks/guides/videos say that yes, it is possible, but the chances are extremely small. Thus, when this situation actually happens after a very long time, entropy decreases, so isn't this a direct violation of the Second Law of Thermo? Assuming that the system is in an isolated vacuum, this also means that there can be no transfer of heat to the surroundings, so there is nothing else that can gain entropy. How is my thought process incorrect? Thanks!
When you say "possible" do you mean something that will actually happen somewhere in the observable universe for long enough to observe? If that is the definition of possible, then violation of the second law is not possible.

Think of the likelihood of as about the probability that the Democrats will win all the seats in the House and Senate next election and continue to do so for the next 1000 years and then divide that by the number of atoms in the earth. That is about the probability that one gram of air will violate the second law for about 1 ms. once since the Big Bang.

AM

jtbell
Mentor
Suppose you have a container with one gas molecule in it. Divide the container into two halves (left and right) mentally. The probability is 1/2 that the molecule will be in the left half of the chamber at a given time.

Next, suppose that there are 2 gas molecules in the container. The probability is (1/2)2 = 0.25 that both molecules are in the left half of the container at any particular time.

Next, suppose that there are 3 gas molecules in the container. The probability is (1/2)3 = 0.125 that all three molecules are in the left half of the container at any particular time.

See the pattern here?

Next, suppose that there is a mole of gas (6.02 x 1023 molecules) in the container. The probability is ##(1/2)^{(6.02 \times 10^{23})}## that all molecules are in the left half of the container at any particular time. Exercise: evaluate that probability.

Suppose you have a container with one gas molecule in it. Divide the container into two halves (left and right) mentally. The probability is 1/2 that the molecule will be in the left half of the chamber at a given time.

Next, suppose that there are 2 gas molecules in the container. The probability is (1/2)2 = 0.25 that both molecules are in the left half of the container at any particular time.

Next, suppose that there are 3 gas molecules in the container. The probability is (1/2)3 = 0.125 that all three molecules are in the left half of the container at any particular time.

See the pattern here?

Next, suppose that there is a mole of gas (6.02 x 1023 molecules) in the container. The probability is ##(1/2)^{(6.02 \times 10^{23})}## that all molecules are in the left half of the container at any particular time. Exercise: evaluate that probability.
Well I understand it's extremely small, but after a long amount of time it would happen. That being said, it just seems to me that the 2nd Law is not 100% rigorous, that it's statistical like stevendaryl said?

Next, suppose that there is a mole of gas (6.02 x 1023 molecules) in the container. The probability is ##(1/2)^{(6.02 \times 10^{23})}## that all molecules are in the left half of the container at any particular time. Exercise: evaluate that probability.
I think the probability would be much less then that, because once you have enough atoms to make collisions likely, such collisions would always be more likely to send an atom to whatever side had fewer atoms at that moment.

Khashishi
If your system is small enough, then it isn't so unlikely for entropy to spontaneously decrease. So the second law of thermodynamics only applies to macroscopic systems.

Jano L.
Gold Member
Well I understand it's extremely small, but after a long amount of time it would happen. That being said, it just seems to me that the 2nd Law is not 100% rigorous, that it's statistical like stevendaryl said?
In classical thermodynamics, 2nd law is a basic assumption derived from experience with macro-systems changing their equilibrium macrostates. It is thought to be a physical law, unless a contradicting evidence is found (which was not to this day).

In statistical physics, the statement of the 2nd law is no longer an assumption, but a statement that is true with probability very close to 1 for system of large number of particles describable by macrostate, provided certain probabilistic assumptions are assumed. If the number of particles is too small, the statement of the 2nd law loses meaning, as there is no macrostate for such system.

anorlunda
Staff Emeritus
Your speculation is on the right track if you scale it up to the size of cosmology and the universe. In his book, "The Fabric of the Universe," Brian Greene speculated that exactly such a statistical fluctuation (improbable event) that you postulate created the universe in a state of low entropy. Since then, the universe has been working its way back to a state of maximum entropy; thus the second law.

You might ask, "A statistical fluctuation in what?" But physics can give no answer. Particles, energy, space, and time may or may not exist outside the universe. We don't know. We can only speculate. In PF we don't do metaphysics.

So wasn't this creation event a massive violation of the second law? Well, we only say that the second law applies post-creation so it dodges the question.

So how improbable is the event you postulate? I say this tongue in cheek -- at least once in this universe's eternity.