# Synchronized Bosons and Entropy.

1. Jul 30, 2011

### dydxforsn

How is it that the tendency for bosons to take the same state doesn't violate rules of entropy? I can understand why Bose-Einstein condensation wouldn't, because that's how the particles take a minimum energy state.

I know lasers work because the photons present encourage other photon involvement (excitation) because of this property of bosons. Is it that this ordered laser beam actually has an increased number of microstates? (that's my best guess) I'm only an undergraduate, so I'm assuming there's more "inner-workings" that I don't know of.

2. Jul 31, 2011

### kith

According to the second law, entropy rises monotonically only in isolated systems. The entropy of a BEC is very low, but to achieve it, you have to cool strongly, therefore heating the environment and increasing the entropy there. The same is true for the laser.

In general, the tendency of a system to go to its ground state can be viewed as a consequence of the second law. If you have an ensemble of atoms in a given excited state and the "empty" radiation field (wich corresponds to T=0), the entropy increases if the atoms emit photons which then occupy states of the radiation field. On the other hand, if you have an ensemble of atoms in the ground state and a thermal radiation field, the entropy increases, if the atoms absorb photons until they reach thermal equilibrium. (as you've mentioned, entropy corresponds to the number of available microstates for a given macrostate)

What the ground state of a given system is, has nothing to do with entropy but is determined by QM. So there's nothing special about the boson case.

Last edited: Jul 31, 2011
3. Jul 31, 2011

Staff Emeritus
"Rules of entropy"? I have never heard of such things, and I suspect that is what is causing you trouble. Why don't you tell us specifically what "rule of entropy" you think is being broken, and we can take it from there.

4. Jul 31, 2011

### dydxforsn

Thanks for the replys, but I still have some questions.

Yes, I agree with that but I'm still not quite sure how it applies to the laser. (I don't doubt you I just don't know about the thermodynamics of a laser. Are atoms being heated to excite them?)

That argument makes sense, except I think that the radiation field NOT being "empty" is what triggered laser activity which would be a tendency towards imbalance. This is my qualm.

See, I'm thinking that, that there is somehow (quantum mechanically) more microstates when the bosons accumulate in the same state than when they're not, which seems weird to me but possible. The only other explanation I can think of is like you said, there must be two systems and one's entropy must increase to account for a decrease in the entropy of the ensemble of laser atoms. I just don't think there should be any problem using the statistical mechanics idea of "entropy" in quantum processes.

Yeah, it may be. I'm operating under the idea that the microstates interpretation of entropy holds in quantum mechanics (systems tend towards the largest available number of microstates), as I've never heard of quantum going against statistical mechanical ideas of entropy, the subjects are frequently united when stat. mech. is used to explain blackbody radiation, etc.