Consider the simplest such system: a gas-filled chamber.
I understand that, were all the gas particles concentrated in one corner, the entropy of the chamber will be lower than the entropy of the same chamber but homogenized.
If so, the two states do not actually represent the same macro-state, hence we will never expect particles in a homogeneous gas chamber to spontaneously segregate.
This can be verified experimentally by trying to separate the gas into distinct regions, one of high pressure and another one with vacuum. The more we try to segregate, the harder it gets showing that this separation will never happen spontaneously.
However, such a chamber is often [erroneously?] represented as pebbles on a board: https://www.youtube.com/watch?v=kfffy12uQ7g But pebbles remain in the segregated state indefinitely, whereas gas particles always homogenize spontaneously and always resist segregation as discussed.
Therefore, can there EVER be any spontaneous fluctuations that lowers the entropy (segregate the content) of such an isolated system?
- 59
- 3
2 Answers
It sounds like you're asking if it's possible for all the random movements of particles through pure statistical chance to to result in one of the infinitesmal combinations of particle positions where the particles are segregated instead of one of the infinitely greater combinations where the particles are not segregated? Yes, it's mathematically possible but you will never see it in your lifetime, or anyone else's, or even the universe's lifetime. I am not a physicist so I don't know for sure how that plays into entropy calculations but think it is considered a spontaneous increase in entropy.
This is at the core of the theory that after the heat death of the universe, over infinite time, things by random chance would happen to find themselves back close together again such that entropy is reduced which would result result in live universe, and over even infinite time, an identical universe indistinguishable from the current one with the same chain of events as the current one (as well as many other infinite very different, and very similar variations along the way).
I don't expect this to be demonstrable, even on small scales unless you do so over time spans so vast that it makes the ultimate life time of our universe looks like literally nothing.
The closest thing is probably a Go board where you repeatedly empty the board and randomly fill the board over and over again until you end up with a combination where all the white stones are on one side and all the black stones are on the other side. Even that would still take nearly forever, even via computer since there are so few combinations where the stones are segregated compared to those where they are not. And this is just 361 moving pieces with very limited degrees of freedom compared to a real system.
- 9,389
Since there is no such law that molecules may not congregate in a corner it could happen but that does not mean that a single fluctuation itself has lower entropy than, say, a more likely one such as in the uniform spatial distribution. Statistical entropy is not about a single arrangement of molecules, rather it is about the "size" i.e., number of similar arrangements.
Following along the same lines, one could say that equilibrium thermostatic entropy is about the constraints that maintain equilibrium. If you allow a change in the equilibrium by changing the constraints then a new equilibrium will establish itself with a new entropy that is larger than the starting one. This formulation of the 2nd law is essentially identical to the usual one.
If you have a cylinder with a dividing wall and only on one side you have gas then punching a hole will let the gas through it and occupy the hitherto empty half. When the gas occupies the larger volume it will have larger entropy but the entropy increase is, therefore, not caused by the molecules now moving in a larger volume but by the act of punching a hole and thereby changing the constraints on the gas.
- 21,193