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Imagine I have an infinitely strong container of volume $v_1$, and I fill it with some monoatomic fluid like liquid hydrogen. I then proceed to compress the walls of the container to reduce its volume by some fraction to $v_2$.

How much force/energy is required to reduce the volume of the container to ~99%, ~50%, then perhaps ~0.1% of its original volume? How might one characterize the various states of matter (presumably plasma) inside the container at different ratios of $\frac{v_2}{v_1}$?

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The term you are looking for is "degenerate matter". Specifically matter supported by a degenerate Fermi gas of electrons (the stuff of white dwarf stars) first and then matter supported by a degenerate Fermi gas of neutrons (the stuff of neutron stars, also called "neutronium"). –  dmckee Sep 9 '11 at 2:43
    
AFAIK hydrogen is not monoatomic. –  valdo Oct 9 '11 at 9:28
    
A plasma is defined as a gas consisting out of free ions and electrons. GAS! And for the rest : energy of compression is integral pdV . –  Georg Oct 9 '11 at 11:17

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This is a bit of a meta-answer but the question is extremely general. The behaviour of a fluid under pressure depends on the specific fluid's phase diagram and temperature. Matter will assume progressively denser configurations to equilibrate with applied pressure. In the case of liquid hydrogen (which I would like to point out is diatomic), well, I was able to find this T/$\rho$ phase diagram on Burkhard Militzer's page (which looks like a great read for high-pressure materials physics). If you trace a horizontal line through the diagram (an isotherm) near the bottom (assuming constant low temperature) you will pass through a mixed gas/liquid phase, a 'conventional' solid phase, and finally, at extreme density, the fabled solid metallic hydrogen, which I think is where dmckee's comment kicks in.

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My impression is that you'd form a solid like metallic hydrogen well before, say, ~95% compression of a fluid. I'm mostly interested in the regime dmckee is referring to, but it would be great to have some hard numbers. –  TheSheepMan Sep 9 '11 at 10:10
    
@ TheSheepMan - This paper will probably be of interest to you. pnas.org/content/107/29/12743.full . Anyhow, wiki says that liquid hydrogen (at 1 bar, I assume) has a density of ~0.07 g cm^-3. At, say, 10^2 K, you would hit the molecular solid to metallic solid transition at a density of 1 g cm^-3. That would represent a 14.3-fold decrease in volume, or 93% compression, I think. The pressures required to get that kind of density are totally insane (note the 1 Mbar (~1 million atmosphere) line nearby and the logarithmic scale). –  Richard Terrett Sep 9 '11 at 12:28

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