The discussion centers on the phenomenon of ionization at low densities, as explained by John Baez. He asserts that all matter, excluding black holes, tends to "sublimate" or "ionize," losing atoms, electrons, and protons even at low temperatures, provided the temperature is above absolute zero. This process is driven by the competition between minimizing energy and maximizing entropy, with the statistical mechanical partition function of hydrogen atoms being divergent, indicating a low probability of binding between protons and electrons in an infinite universe.
PREREQUISITESPhysicists, chemists, and students of thermodynamics or statistical mechanics seeking to understand the effects of ionization at low densities and the underlying principles of entropy and energy minimization.
... everything except the black holes will have a tendency to "sublimate" or "ionize", gradually losing atoms or even electrons and protons, despite the low temperature. ... If you take a box of hydrogen and keep making the box bigger while keeping its temperature fixed, it will eventually ionize. This happens no matter how low the temperature is, as long as it's not exactly absolute zero — which is forbidden by the 3rd law of thermodynamics, anyway.
This may seem odd, but the reason is simple: in thermal equilibrium any sort of stuff minimizes its free energy, E - TS: the energy minus the temperature times the entropy. This means there is a competition between wanting to minimize its energy and wanting to maximize its entropy. Maximizing entropy becomes more important at higher temperatures; minimizing energy becomes more important at lower temperatures — but both effects matter as long as the temperature isn't zero or infinite.