Is the Heat Death of the Universe necessarily permanent?

It is commonly reported on popular science venues that the expected end of the Universe will be a slow Heat death. The basic idea is outlined here, at Wikipedia.

I wrote a long article, so if you are already familiar with physics and entropy, you can probably skip all of this and head to the final question. If not, it might be helpful to follow my reasoning.

The Heat Death scenario depends on the idea that entropy must always increase; if there is a localized decrease in entropy it is only at the expense of an increase of entropy somewhere else in the Universe. The process of increasing entropy also decreases the amount of free energy available in the Universe, as isolated systems of high order and potential energy spontaneously flow to states of less order and greater entropy, typically in the form of heat, which cannot be easily converted back into a useful form of potential energy.

I never liked the definite claims of the second law of thermodynamics. I am much more satisfied with the statistical approach, which merely states that increasing entropy, or making the number of states more heterogeneous and less homogeneous, is a highly unlikely process in the case of large molecular aggregates (we note that 1 liter of water has 3.34279307 × 10^25 molecules).

This is clearly described as a function of probability. A single state, where gas molecules are initially localized in a room with no external barriers trapping the gas, will naturally evolve to a homogeneous state merely because the mass of molecules don’t have any specified trajectory, and the state defined as having the most identical conformations will be the most likely state. This seems intuitive. More importantly, this is merely a description of what is most likely to occur, not what must occur.

The Universe supposedly contains 10^80 atoms; it started in a state of high density and naturally evolved into a more diffuse state. Incidentally, in the process of expanding certain areas of the Universe began to aggregate, ultimately allowing for stable solar systems to form, and thereby life.

As the Universe continues to expand and its entropy continues to increase all the potential energy of the Universe that is useful in propagating life and other interesting processes will be converted into heat. According to the second law of thermodynamics it will be impossible for this heat filled Universe to spontaneously aggregate into a higher lower state. This means the Universe will die.

That’s assuming that it’s absolutely impossible for the total entropy to decrease, which I think is a faulty assumption. Looking at it from a statistical point of view the Universe could potentially revert back to a state of lower entropy, given enough time. Since the Universe will have an infinity of time to generate this lower entropy state, no matter how unlikely the process may be, doesn’t that imply that it would necessarily be inevitable?

In fact there is documented examples of processes that really do seem to violate the second law of thermodynamics. An example found here:

In short, given an infinite amount of time can the entropy of the Universe decrease so substantially as to produce conditions that are viable for galaxy formation / life?



Lots of assumptions need to be made. However, one of your assumptions was that the universe is expanding. That means that more and more of the matter in the universe will move so far away that it cannot affect the rest of the matter. (Just as there already exists matter from the big bang outside the observable universe.)

So you don’t have a full universe anymore. You have a decreasing fraction of those 10[sup]80[/sup] atoms. At a certain point you have nothing but a few isolated photons with nothing to interact with. That means a reversal of entropy becomes impossible given your scenario.

I get that you think it would be inevitable for some bumps up into lower entropy states, but how is it even remotely possible that the entire universe would do something like that? And why would it be meaningful, when the statistics say that it will just go back to a higher entropy state after a while? A universe in heat death is so far down the entropy ladder that even a couple of random jumps up won’t make it productive again.

Ultimately, I think heat death is going to be redefined many times. Until we understand dark energy and dark matter, we’re just not in a good position to project what the universe will be like in 10^100 years.

A reversal of entropy is not only insanely unlikely, but becomes even less likely as time goes on, in such a way that, even allowing for infinite time, the chances of it ever happening are still insanely small.

The universe may be winding down, but the process by which it came into existence in the first place — something that we do not now have much of a handle on; “a massive vacuum fluctuation” is as creditable an explanation as any, which basically amounts to “it’s here becasue it could be” — may be a non-unique event. If event is the right word.

Perhaps “universe” springs into existence (bringing its own spacetime with it) over and over “again”, or all the “time”. (Questions about whether to consider them to come “after” each other or to exist “concurrently” are probably not even applicable in the ways we usually construe such things)

This was a beautiful story, and exactly what I had in mind when I was thinking about entropy. thank you so much.

Does the Poincaré recurrence theorem apply to the question? The recurrence takes a long time but

No, since the energy of the Universe as a whole is not conserved.

Wha…? Since when?

Is the Universe Leaking Energy?

Let there be light!

Since the big bang.

This is true. In the context of general relativity, “energy” is ill-defined.

What we know about the Universe now is that it is expanding, and it consists of:

–4-5% normal matter, which dilutes (gets less dense) as the volume of the Universe increases,
–20-26% dark matter, which dilutes the same way as normal matter,
–about 0.008% radiation (photons), which dilutes faster than normal matter, because in addition to the number density going down the way normal matter does, the wavelengths of the photons stretch, causing them to lose energy. (FWIW, if the Universe ever contracted instead of expanded, the energy would rise.)
–the rest (adding up to 100% total) dark energy, which doesn’t dilute at all. In other words, as the Universe expands (and appears to increase in volume), the dark energy density remains constant, so it looks like dark energy is just appearing out of nowhere.

Based on this picture of the Universe, the heat death is inevitable. If you want a different fate, you need to invent new physics, for which there is presently no evidence.

I thought The Big Rip was also consistent with current observations.

True, and in fact if we’re near the outer edge of the error bars, it might come much, much sooner than any of the other end-of-the-Universe scenarios, perhaps even in a matter of millions of years rather than billions. But the evidence is also still solidly consistent with constant-density vacuum energy (by far the simplest assumption), and I don’t think anyone’s come up with a theoretical framework that can even qualitatively lead to phantom energy.

The Big Rip is an interesting scenario, and one that lots of wiggle-room exists for.

But it would, first off, require some new and unexplained physics beyond dark energy simply being a cosmological constant. Nothing is theoretically compelling about a Big Rip model, either, as they’re all extraordinarily ad hoc.

Of course, the Universe simply does what it does, and if we found that the dark energy equation of state, w, was less than -1, then the Universe would head down the road to a Big Rip.

But when I started studying dark energy, the constraints were -0.5 < w < -2.5

Nowadays, the constraints are something like -0.91 < w < 1.12

It only needs to be slightly less than -1 to give a Big Rip, but the evidence isn’t really pointing there in any reliable way, and never really has. Improvements are slow, and motivations for it are slight. My personal slant on it is I don’t believe there are any interesting deviations from w=-1 happening at a level that’s going to be observed within our lifetimes.

Can you actually give a formal proof of that claim? To me, it seems that anything that could happen, will happen, given enough time.

Anyway, I am not sure that the heat death will really happen. It will take a bit of explaining. First, the free energy will never actually be 0, only approach it asymptotically. That means that motion will not stop, only get arbitrarily slow. What started me thinking on this was something I read somewhere that there is no minimum energy needed for computation; The less energy you use, the slower it goes. I assume the same is true of us; the less free energy we have, the slower we (or our successors) can move. But if we slow down and both our minds and our computers slow down correspondingly how would we notice. I guess light speed would appear to get faster and faster, but it is already essentially infinite as far as we are concerned, so again there would not seem to be any practical effect. Since there will always remain some free energy, I do not see, in principle, why this couldn’t continue indefinitely.

What? No one’s mentioned Loschmidt’s paradox and the fluctuation theorem yet?