Water can evaporate with no external energy input, as long as it is above 0K (as the temperature decreases it will take more and more time, but is not impossible) as molecules of water have a probability of getting enough kinetic energy from their neighbouring molecules to escape and evaporate. So if that is possible, why wouldn’t there be a chance that a molecule of air/gas interacts with their neighbours and statistically get enough energy to be ionized (even if it takes some time and it’s rather short lived)?

I asked a similar question in another forum, and this is what I got as an aswer:

If the OP was referring to air in an Earth/ Earth like atmosphere, then in a classical physics sense, there are multiple energy inputs causing ionization of the air so it is not spontaneous ionization. If we are talking about Quantum Mechanics, then we cannot speak in absolutes, only in probabilities. In a closed Quantum system, the net charge must remain the same, so if an atom/ molecule loses an electron, another must gain an electron. This will be through virtual particle/ anti-particle pairs appearing in the Quantum field. So while an individual air particle could possibly be affected, an adjacent air particle will be affected in the opposite way leaving the system in a net zero change in energy and a near instantaneous neutralization of any ionization. Again, practically, no spontaneous ionization. In an Earth/ Earth like atmosphere, there is so much Energy being distributed through the atmosphere, any Quantum effects of air molecules being ionized are statistically not zero in Universal time scales, it is highly not probable in human time scales. So again, for practical purposes, no spontaneous ionization of air will occur.

However, this explanation sounds a bit strange to me (the part about invoking particles/anti-particles pairs to exolain ionization seems to be a bit-off, but I may be wrong).

Is it right? If it is, does it mean that random motions of gas molecules due to e.g. brownian motion will never produce ions?