>The glib answer here is that there's really no such thing as the 2nd law when you're talking about a small number of individual fundamental particles. The statement "entropy never decreases" is actually a purely statistical claim, and it only rises to its usual level of essentially unbreakable validity when you're dealing with macroscopic numbers of particles
All the fundamental laws of physics, including the Schrodinger equation, follow the 2nd law or in other words they describe application of 2nd law to the given area of physics, i.e. they express "entropy never decreases" principle in terms of the objects of that physical area.
>"there is less "phase space" available (fewer possible momentum states)"
ie. less entropy :)
>an electron and positron are electrically attracted to each other and will naturally tend to meet up to annihilate
2 particles having negative and positive charges - less entropy than the entropy of 2 resulting neutral particles. Attraction (getting closer - increasing entropy) and annihilation (erasing the charge difference - increasing entropy) are in full compliance with, and i'd say direct manifestation of, the 2nd law :)
My glib objection was not to the notion of there being less entropy in one state than the other, but in calling the result "the 2nd law of thermodynamics" in cases like this.
The phase space argument means that it is less likely for the system to wind up in the e-/e+ state than in the 2-photon state, and calling that a manifestation of entropy is entirely sensible. But in general, there's a non-negligible chance that the system will wind up in the e-/e+ state anyway: it's very much a possibility (and becomes even more so when the total energy is greater).
I usually reserve the term "2nd law" for cases where the probabilities are tiny enough that it's essentially impossible for the entropy to decrease by any remotely significant amount. That level of certainty typically requires systems of many particles, not just one.
this is why i drop "of thermodynamics" because that calls for many-particles situation. Referring to "2nd law" i mean the generic "non-decreasing" entropy principle, and i'm wondering about its violations - mainly i believe that there are no violations of it in the physical world (as the known laws of physics seems to obey/describe that principle), and this is what prompted my original question about virtual particles.
I understand that pure statistical interpretation allows for non-negligible chances of the violations. What i'm wondering about is whether strong, non-statistical, interpretation is valid - ie. whether anything looking like a violation is just a non-complete calculation. After all it is pretty fascinating that entropy principle applicable (at least in statistical interpretation) on all scales - from the whole Universe down to quantum systems and for all the physical laws/forces.
I guess that I have trouble imagining how any law of physics that I know of would enforce such a rule. The whole point of statmech is that the 2nd law is an emergent phenomenon: it's not a separate influence on the universe independent of the known fundamental forces, but rather a consequence of how those known laws play out in cases with many particles and/or states. What you're suggesting is some additional influence at microscopic scales, and that seems quite implausible to me. (Just how strict are you imagining this rule would be? If two states had phase space volumes in a 51/49 ratio, are you suggesting that the system would always pick the 51?)
It's hard to list intuitive counterexamples to your suggestion here, since anything intuitive is by definition part of a macroscopic system that would obey the 2nd law anyway. But... for instance, are you saying that you don't believe in the Maxwell speed distribution in an ideal gas? If no molecular interaction could ever take a system from a larger to a smaller total phase space, then every molecule in an ideal gas should eventually converge to the RMS speed. That's a clear experimental prediction, and I'm pretty sure that the usual answer has been well-tested (both explicitly and implicitly).
>The glib answer here is that there's really no such thing as the 2nd law when you're talking about a small number of individual fundamental particles. The statement "entropy never decreases" is actually a purely statistical claim, and it only rises to its usual level of essentially unbreakable validity when you're dealing with macroscopic numbers of particles
All the fundamental laws of physics, including the Schrodinger equation, follow the 2nd law or in other words they describe application of 2nd law to the given area of physics, i.e. they express "entropy never decreases" principle in terms of the objects of that physical area.
>"there is less "phase space" available (fewer possible momentum states)"
ie. less entropy :)
>an electron and positron are electrically attracted to each other and will naturally tend to meet up to annihilate
2 particles having negative and positive charges - less entropy than the entropy of 2 resulting neutral particles. Attraction (getting closer - increasing entropy) and annihilation (erasing the charge difference - increasing entropy) are in full compliance with, and i'd say direct manifestation of, the 2nd law :)