I never did quite figure this out and all the people I asked seemed to be either non-commital or just plain contradictory (the same people who claimed that there was no such thing as a perfect vacuum).
What I want to know is, Are the 4 laws of thermodynamics absolute in nature (as in, this will NEVER EVER happen) or statistical (as in, given enough time, there is an INCREDIBLY small chance that this will happen but it usually doesn’t)
Law 0: If body A is in Equilibrium with body B and body B is in equilibrium with body C, body A will be in equilibrium with Body C.
See no problems with this one being absolute, basically stating that the equivilance relation of equilibrium is transitive.
Law 1: The energy of a close system is constant
I know about quantum fluctuations but is it possible that the positive quantum fluctuation can ever be more than the negative?
Law 2: The total entrophy in a closed system will always tend towards a maximal bound (creationists, please dont kill me)
This is the one I have trouble with, As far as I know, it is statistical yet it always seems to be stated as an absolute. ie, if you had a box filled with air, there is a SLIGHT chance that ALL the air atoms will end up in a 1mmx1mmx1mm box in the center and leave the rest in a complete vacuum. In practice, however, this never happens.
Law 3: Absolute Zero is the very minimum energy state a system can be in
This one is statistical. If you have a hot gas in one side of a container separated by a conductive membrane from a cold gas in the other side there is a non-zero probability that the hot gas will get hotter, in the sort run, and the cold gas will get colder. How?
Well, the molecules of both gases have energy distributed about some average. It is just barely possible that most of the collisions will be between the hottest molecules of the cold gas and the coldest molecultes of the hot gas thereby transfering energy from cold to hot. But don’t bet on it ever happening.
Or, as Isaac Asimov put it, “It’s possible for a kettle of water to freeze solid while the fire beneath grows hotter; but if the entire known universe were filled with kettles of water over fires, it wouldn’t happen during the entire lifetime of the universe.” (paraphrased)
IMHO (and this is just MHO), there are only two descriptions of natural phenomena that nay be considered absolutely true in the pantheon of scientific ideas: The first are the laws of thermodynamics (including the 2nd Law); and the second is the Darwin-Wallace idea of evolution by natural selection.
The 2nd Law of Thermodynamics is certainly formulated as a statistical proposition. As Asimov and others have noted, there is no a priori reason that a container of water at room temperature (not to mention one above a Bunsen burner) COULD NOT suddenly fuse into a gob of ice…but the fact is that it has never been observed to do so and never will.
As regards evolution by natural selection, this idea is so powerful that it must apply not only to living organisms in our world, but surely would apply to ANY self replicating entities (including computer programs—eg “The Game of Life”—in ANY imaginable universe.
Is there any reason why statistical laws can’t be absolute? Sure, there’s a non-zero chance that your kettle can freeze, but just keep on waiting. Eventually, it’ll still equilibrate, in a finite amount of time.
I’m know sure how to precisely define a statistical law vs. an absolute law. Thermodynamics is by definition the study of how very large numbers of atoms behave as a whole. It can only make statements in terms of probabilities. However, this doesn’t mean one should make statements like “could happen, but probably won’t” with respect to things like water freezing on a stove. One can calculate the probability of that happening, and it really doesn’t make sense to call it non-zero. At some point, zero to (e.g.) 10[sup]10[/sup] decimal places is zero. Period.
Putting a statistical range on something doesn’t, in my opinion anyway, make it non-absolute. The predictive power remains the same. And for the systems studied by thermodynamics, the number of degrees of freedom in the system (e.g. the number of molecules in a glass of water) are so large that the probability of anomalous fluctuations is never greater than zero within more decimal places than my definition of zero requires.
One of the things you begin to explore when dealing with the laws of thermodynamics (namely the second) is what zero is. I seem to remember that a probability of 10^-19 was considered for most purposes to be zero.
That was horribly done… It’s not a probability of 10^-19 at all. I failed to state conditions and so forth. In any case, I’m not able to access my thermodynamics text at this time, so either someone will have to jump in and give the proper conditions, or you’ll have to wait a bit.
They are statistical, of course. The number of degrees of freedom in any sizable physical system however, as pointed out by Giraffe, is so large as to make them virtual certainties. But I don’t think that allows one to reasonably discount the basis of the laws themselves.
But what about conservation of energy? It was always to my understanding that this WAS absolute. ie, if you have an insulated box full of air, it could not ALL get cold, but it COULD get warmer in one place and colder in another. Is this statistical or absolute?
Shalmanese is right, classically speaking: conservation of energy IS absolute, while increasing entropy is a statistical effect. If you’re going to do work, the energy HAS to come from somewhere, and vice versa. possible that energy could flow from a colder object to a hotter, but really unlikely (in the sense of ‘no chance in hell or anywhere else’).
In relativeity, this is still true, though sometimes the definition of energy is a little different than the classical definition.
And of course in quantum physics, most of what we think of as absolute laws turn out to be statistical effects. Though energy is still conserved, I believe.
Interesting question. I think Quercus is right that conservation of energy is absolute. Taking the “insulated box” as the universe as a whole, in the hypothetical spontaneously freezing water is the entropy of the universe increased or is the process strictly reversible? The energy loss that freezes the water goes into the motion of the colder molecules of the rest of the universe without the conversion of energy from one form to another, say chemical to heat and heat to mechanical.
Anyone who is good at statistical mechanics in the audience?
Quercus IS right, as far as I know. Certainly, it’s true that we could in principle write down a huge collection of Feynman diagrams to describe any process you care to name, and since every Feynman diagram conserves energy (at every point in the diagram, no less!) it should follow that as long as are talking about the universe as a whole, energy is conserved absolutely. Of course, in any subsection, energy needn’t be conserved at all.
I’m not a stat mech guru, but it seems to me that if we envision the possibility of spontaneously freezing water, we must also envision the possibility of spontaneously melting ice, so spontaneously freezing water ought to be reversible, oughtn’t it?
I’m not a statistical mechanics guy either. On thinking some more about it though, reversibility would require perfectly “elastic collisions” between molecules. However, when the molecules approach each other the first thing that would happen, I think, would be redistribution of the charge in the outer shells of the atoms. This would be an acceleration of electric charges which results in EM radiation, probably somewhere in the long IR. Energy would be lost as heat and to be distributed randomly around the universe. So it couldn’t be recovered by the original particles and the collision wouldn’t be “elastic.”
That’s my take anyway.
We see spontaneously melting ice all of the time. And we will continue to do so as long as there is material around that is above the freezing temperature.
Well yes, of course we see spontaneously melting ice above the freezing temperature. We also see spontaneously freezing water below the freezing temperature, eh? My basic take on it is this: the liquid phase is a higher entropy state than the solid phase. Ergo, spontaneous freezing can’t possibly be irreversible from a purely entropic standpoint.
Well, I could imagine that if there was an ice cube sitting in a freezer, the air not around the ice cube might spontaneously drop down to 1 degree K and the air around the ice cube would warm up to whatever and melt the ice cube.
What I am really intruiged about now:
Imagine you have a bounded, fixed size universe. Even after its eventual heat death, there is still hope for intelligent life since stars could spontaneously appear. It doesnt matter if the probability is 10^100 or 10^10^100, the life of the universe is INFINITE so theoretically, anything that still conserves energy CAN AND WILL happen.