Thermodynamics question: Gibbs free energy and the Big Crunch

I’ve seen the Gibbs-Helmholtz equation, dH = dG + TdS, and am given to understand that dG is energy that is available to do work, but I’m not sure how or whether it might apply to the questions I have.

Suppose the universe has enough gravity to pull itself back into the Big Crunch collapse. Does this process restore the amount of DG that was lost through entropy as the universe expanded? If so, how? If not, isn’t there a limit to the number of times the universe could Bang and Crunch before entropy is 100%? If so, how many times?


I don’t know a definitive answer to your question but realize that what happens inside the Big Crunch singularity (or any singularity for that matter) is anybody’s guess.

I mention that since while I don’t think the thermodynamic arrow reverses itself towards a Big Crunch once the crunch is complete it may very well get ‘reset’ (for lack of a better word). Or maybe not.

My point is I don’t think you could calculate how many Big Bang/Crunches you’d get since our math utterly falls apart at the singularity.

Okay, that’s fair enough. Thanks, Whack. I guess I will settle for information on whether the arrow can be reversed and if so, a description of the mechanism that would do it.

Hello- this is all way over my head. But - wouldn’t the Big Crunch necessarily have zero entropy - since all the substance of the Cosmos is at one (the only )point?
How could you have any distinction between dispersed energy and energy available to do work in those conditions?
If the Cosmos is contracting toward a Crunch won’t the thermodynamic arrow reverse itself - since available energy is constantly increasing?
Would time run backward?
Please forgive my ignorance :slight_smile:

[nitpick #1]
Lib, if I recall my thermo correctly, the energy available to do work isn’t the Gibbs free energy, it’s the Helmholtz free energy. This is given by A = U - TS = H - PV - TS = G - PV.
[/nitpick #1]

[nitpick #2]
Also if I recall my thermo correctly, the equation you have as written is only true for constant temperatures, and the universe doesn’t have constant temperature, of course.
[/nitpick #2]

All that aside, you ask an excellent question, and I have no idea what the answer is. It seems intuitively obvious that a Big Crunch would result, if nothing else, in a decrease in the total entropy of the universe, which is strictly verboten, so either I’m failing to appreciate a fundamental point about what the entropy of the universe is, or thermodynamic laws don’t work in extreme situations like a Big Bang/Big Crunch, or both. And I’m not really sure what the answer is.

It seems like what has to happen if the Big Crunch picture is correct is that the Helmholtz energy has to be reset. How that happens, I don’t know. But a key point is that the Helmholtz energy tells you how much energy is available to do external work, if I remember correctly (Atkins is a little vague on this point, and I can’t find my notes). If it’s the amount of energy for external work, then there’s really no problem, as of course the universe by definition can’t be involved in doing external work.

I realize this is profoundly unhelpful, but it’s the best I can do right now. Sorry.

I’m not sure of the accepted answer (if there is one), but contrary to intuition I don’t think that a Big Crunch has to result in an entropy decrease. For example, the entropy of a black hole, where all the matter is apparently “compressed” (in quotes, because it’s not clear what really happens there) to a singularity, is actually very large. (This was first understood only thermodynamically. Only recently have theorists begun to understand how to derive this result in a statistical-mechanics sense, by counting states near (but outside) the event horizon of the black hole.) If the Big Crunch acts like a black hole the universe’s entropy may continue to increase even as it collapses toward a singularity.

Thanks, G8rguy and Omphaloskeptic. I didn’t really mean to say that the Big Crunch itself would result in an entropy decrease. As I understand it, the entropy decrease has already occured in the normal course of the universe’s existence.

Recently there was possible evidence that entropy in quantum size particles might actually decrease. Does that allow for an out in this case, given that the crunch would have to pass through a quantum state before we lose track of the physics

Lib - and others,

How does light itself come into play in the process?
Does the emmitted light from the stars get recollected in the Big Crunch, or is it lost? And finally, does it even come into play in this (Libs) OP.

I just noticed that my last post used “decrease” in every instance where I meant “increase”. A thousand apologies to everyone.

Maybe the following will help. I’m liberating the quote from a thread I started awhile ago. Ring had provided this quote and the link in that thread. Follow the link for even further detail.

Fantastic information, Whack. I believe that answers my question nicely, thanks.

I always thought that the Gibbs free energy formula applied specifically to chemical reactions. Also, deltaH and deltaS are usually determined/defined in a CLOSED SYSTEM which the universe is definitely not.

Well, G = H - TS applies everywhere, as it’s just a definition. You can obviously differentiate this to get what Lib provided us with, although he left out a term -SdT which is usually dropped in chemical applications because the Gibbs free energy is most useful in constant temperature situations.

But the laws of thermodynamics are applicable pretty much everywhere, except possibly in cases like black holes and the like (although even there, there’s suggestions that they apply). And the universe is most definitely a closed system. In fact, it’s an isolated system, which is an even stronger condition.

Would you care to explain THAT in a little more detail?

Sorry; everything I know about thermodynamics comes from chemistry, which has skewed my thinking. In Classic P-Chem, when determining quantities such as Enthalpy, you have your “system,” which consists of known amounts of reactants inside a closed box (a calorimeter, for example) in order to isolate it from everything else-which technically includes the universe.

When trying to measure the enthalpy of the universe, this analogy breaks down; I mean, where would you get a calorimeter big enough to fit everything, and further, what would be outside the box?

Just so; the universe is the box.

While we’re on the question: Was the mega-singularity which banged in a state of 0 entropy, 100% entropy, or not measureable, becasue we can’t predict the behavior of all mass/energy in one place at one time?

How do we know if there was a mega-singularity? (HINT: we don’t.) There are more than one model to explain the cosmic egg. We do, though, know that since entropy in the universe is increasing that it was lower earlier and (presumably) the lowest it can ever get at the big bang. However, this is a bit of a strange thing(like dividing by zero) since the temperature is also increasing. Having a hot, well ordered crystal is just not something you’re used to, but then when was the last Big Bang you saw in infancy?