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we know that stars fuse hydrogen into helium starting at 3 MK; 13 MK in the Sun's core; carbon fusion starts at above 500 million K, and silicon fusion starts at over 2700 million K for comparison; we know fusion stops at iron, because a star has to use more energy to fuse that than it gets back; so heavier elements are created mostly in a supernova (but also possible in small quantities by special processes like neutron capture); finally sun-like stars end up as white dwarfs, bigger stars as neutron stars, quark stars, black holes; and black holes ultimately convert themselves into radiation, in the far distant future when the stable black hole mass limit goes up high enough that even the most massive black holes evaporate;

http://en.wikipedia.org/wiki/Vacuum_Diagrams

so my question is, will it be like Stephen Baxter said, that in the future only radiation will be left in the universe? Specifically, is there a natural process out there by which hydrogen is spewed into the cosmos, converted back from heavier elements, to regenerate the fuel for stars so that they may shine in the far distant future as well?

Of course we don't need to worry about this for the time being. This is only considering our concern with what will be 10^70 years from now.

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It is not possible to split a larger nucleus into hydrogen nuclei without expending a greater amount of energy that you receive back. This is because Hydrogen has (by far) the lowest nuclear binding energy per nucleon (protium has zero nuclear binding energy, though deuterium and tritium do have some). Therefore, such a process would decrease the entropy of the universe - a violation of the laws of thermodynamics.

Nuclear binding energy curve

I could not speak for if these laws would still hold true were there a "big crunch" (though current observations support an expanding universe).

There is a scenario called heat death, where the universe simply has no energy left to do anything - that is, everything is completely uniform. There would be no gradients or anisotropies in the distribution of energy or matter.

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My question to you is the following: Does nuclear decay necessarily decrease the entropy of the universe? I think the answer is no, and if it is no, there are many ways for heavier atoms to decay into Hydrogen (see my answer below). It may not compare to the rate of fusion processes occurring in the universe today, but in the distant future it may be the only possibility. –  astromax Oct 31 '13 at 12:17
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@astromax - A heavier atom may decay into tritium (which then decays into helium-3) but I don't think anything can decay into protium. Any spontaneous decay will decrease entropy because it must release energy. A universal decay to light elements would release energy (because far less energy is tied up in binding energy), thus decreasing entropy. A state of maximum entropy in the universe would occur when everything has turned to iron. (this is far from my area of speciality, so caveat emptor!) –  Moriarty Oct 31 '13 at 14:27
    
Hmm, I'm not really sure I follow you. I don't know how the entropy of the universe (assuming it is a closed system) would change due to decay processes. I did however talk to my colleagues and the consensus seems to be that the universe may end up being black holes, radiation, and neutrinos as t goes to infinity. The logic here is that even all of the larger stable atoms (Iron is the end point for fusion, and Lead is really the end point for natural fission processes) will eventually fall into black holes given enough time. –  astromax Oct 31 '13 at 20:58
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@astromax I also read about the big rip where even atoms will be torn apart; maybe the universe could be like a bubble that will burst; but, I don't think that things flying apart will cause them to break down at the subatomic level; says here at the bottom wmap.gsfc.nasa.gov/universe/uni_expansion.html that the universe expands by 70km/sec/mpc; if the universe has 13.7G lightyears radius = 4202 mpc then 70 * 4202 = 294140km/sec = almost 299794.458km/sec(lightspeed)so for all its acceleration, expansion is kind of asymptotically reaching its max,lightspeed,so unlikely to rip atoms apart –  jmarina Nov 1 '13 at 16:42
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@astromax, good point questioning whether the universe is a closed system; according to Brian Greene's The Elegant Universe book/movies the strong/weak nuclear forces and electromagnetic are in this universe, but gravity can loop outside what we perceive as 3D+time spacetime and only part of it is here, so gravity could enable interaction with multiverses –  jmarina Nov 1 '13 at 16:52

There are a couple of relevant questions one would want to ask:

1) Do protons decay, and if so, what do they decay into? The answer appears to be no, or at least the theoretical lifetime of the proton must increase as a results of these experiments. If they do, eventually the universe could end up in a state of radiation (and dark energy, and dark matter, unless they also decay).

2) Is Hydrogen a bi-product of any natural decay process? Below is a table of all known nuclides.

isotopes

As you can see, the majority of the elements (not necessarily by number or mass in the universe) do decay through some type of process. There exists a 'stable' ridge (called the island of stability, surrounded by the sea of instability) of elements which will happily exist forever.

The question is, which modes of decay produce protons (Hydrogen nuclei)? Well, there is proton decay (not the proton itself decaying), which is colored in red, though I have to admit that I don't know exactly what this refers to. Fission bi-products are gamma rays (high energy photons), neutrons, and daughter nuclei (see Decay chain). Though, I should mention that free neutrons produced from this type of radioactive decay are not long lived, decaying into a proton and an electron (this process takes on average approximately 11 minutes). By this logic, also isotopes which decay by emitting neutrons, colored purple, would also eventually produce protons. $\beta^{-}$ and $\beta^{+}$ refer to the beta decay process, where the minus sign refers to the emission of an electron and the plus sign refers to the emission of a positron (the anti-particle of the electron). $\alpha$ decay is the emission of a Helium nucleus, which is stable.

Now, given that there are ways for heavy elements to naturally produce protons, the question I would ask is what is the rate of these processes in the universe compared to fusion processes occurring at the centers of stars. I'm not sure that I could give you an answer to this question (or even point you to the appropriate material), but in principle these rates are known. I'd imagine that it'd be quite a lot of bookkeeping to get it correct.

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Wikipedia says about protons in nuclear decay: »Shortly after the discovery of the neutron in 1932, Enrico Fermi realized that certain rare beta-decay reactions immediately yield neutrons as a decay particle (neutron emission). Isolated proton emission was eventually observed in some elements.« –  Arne Oct 30 '13 at 21:45
    
Interesting - I've never heard of that type of decay process. Maybe it's not common. –  astromax Oct 31 '13 at 1:43
    
I like this answer(upvote), the diagram is enlightening, but cannot choose 2 answers unfortunately. en.wikipedia.org/wiki/Abundance_of_elements here we see that hydrogen and helium are 98% of all baryonic matter, so not much decay going on now. But in the far future, I agree, natural nuclear decay could likely be the dominant source for H/He like you said in your comment above. I looked up the speed of an alpha particle, and it seems like it is around 5% of light speed, 15000-20000km/sec depending on energy, so it may be going too fast to gravitationally collapse and form new stars. –  jmarina Nov 1 '13 at 16:20

It seems that primordial black holes produce anti protons, and it is implied in the linked article that they are capable of producing all kinds of other particles. So maybe even protons.

Also, I guess that during natural fission or nucleues collision reactions, there may be fragments being produced that are also single protons.

Cosmic rays seem to consist primarily of protons. The question is, whether these protons were produced in the big bang, or if they stem from other sources. The article states that lots of cosmic rays stem from supernovae. However, this does not answer the question if the protons were produced in the supernova from heavier elements.

Since I am not an astrophysicist, I am gladly waiting for comments or other answers!

Edit: I read about another mechanism on how to create electrons and protons: Two-Photon interaction. I cite the Wikipedia article:

The law of conservation of energy sets a minimum photon energy required for creation of a pair of fermions: this threshold energy must be greater than the total rest energy of the fermions created. To create an electron-positron pair the total energy of the photons must be at least 2mec2 = 2 × 0.511 MeV = 1.022 MeV (me is the mass of one electron and c is the speed of light in vacuum), an energy value that corresponds to soft gamma ray photons. The creation of a much more massive pair, like a proton and antiproton, requires photons with energy of more than 1.88 GeV (hard gamma ray photons).

First calculations of rate of e+–e− pair production in photon-photon collision was done by Lev Landau in 1934.1 It was predicted that the process of e+–e− pair creation (via collisions of photons) dominates in collision of ultra-relativistic charged particles—because those photons are radiated in narrow cones along the direction of motion of original particle greatly increasing photon flux.

In high-energy particle colliders, matter creation events have yielded a wide variety of exotic heavy particles precipitating out of colliding photon jets (see two-photon physics). Currently, two-photon physics studies creation of various fermion pairs both theoretically and experimentally (using particle accelerators, air showers, radioactive isotopes, etc.).

So, in small amounts electron-positron pairs and proton anti-proton pairs should be created by soft and hard gamma radiation respectively (or other Fermion particles). The problem here again is that this event will happen only very rarely, not significantly producing new matter. The article goes on to say that this was the method in which matter was created during the Big Bang. But only one in $10^{10}$ Fermions would have survived to form the current matter in the universe.

All in all these processes will probably be not enough to form new stars.

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ok so I would like to clarify that I'm not picky about whether the hydrogen is generated from heavier elements; if it comes from other sources that is good too; what I want to get at is see whether the fuel for stars can be renewed so they can keep on shining; I would think a primary problem with protons from cosmic rays (good idea btw, upvote for that), although a hydrogen atom is a proton and an electron, if it travels at a significant fraction of the speed of light it would, I expect, find it difficult to be affected by gravitational collapse in order to form a star –  jmarina Nov 1 '13 at 16:09
    
Motion is relative. Maybe there'll be other protons / hydrogen atoms moving in the same direction with the same speed... I think the entropy argument from the other answer is best. The universe is just simply going to shreds -- very slowly... –  Arne Nov 1 '13 at 16:57

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