This is not true, in quantum mechanics at zero kelvin (so in its fundamental state) a system has a non zero energy. See this: https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator#Ha...
I think in that case you reach a paradox because temperature is a quantity (typically) defined in thermodynamics, i.e. systems in equilibrium. A metastable glass is not in its ground state, therefore not in equilibrium, therefore not technically within the purview of thermo. This might seem like a cop out, but a similar question was asked in my qualifier. The answer, glass is not technically described my thermo and at 0K the whole thing breaks down 
Sure we still talk about entropy and temperature of glass, but it's stretching the definitions.
Another way to look at it, though, is that at 0K there is only one state available to the system (even though it is a glassy one). Therefore call the glass a new state of matter, and set S=0. If that feels weird because it's not the ground state, consider that glass' constituents, Si and O, are not in a ground state either, that'd be Fe. You don't have any problems dealing with metastable Si and O, do you? Either way, 0K makes no sense!
Also, it's weird (actually wrong) to even think about materials at 0K. In classical thermo your heat capacity is zero. In modern physics your atoms' "positions'" are fully determined, therefore their "momentum" is fully undetermined. So 0K is a state that makes zero sense.
 I forget the question. I think it was like this: the entropy of glass has a greater slope than the crystal, therefore, if you cool the glass low enough it will achieve a lower entropy than the crystal. How can a glass have lower S than its crystal state?
Especially this might interest you:
"A classical formulation by Nernst (actually a consequence of the Third Law) is:
It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolute-zero value in a finite number of operations."
There isn't any fundamental energy cost imposed by physics here, however. Both because 1) bit flipping can be done in a logically reversible way, just go systematically from 0 to 2^256 - 1 so Landauer's assumptions do not even apply 2) Landauer's idea has been criticized for being vague/badly reasoned. Most weirdly, Landauer assumes that erasure of a bit register in general requires that thermodynamic entropy kln 2 per bit is acquired by the environment. It seems people are confused and can't distinguish information entropy and thermodynamic entropy here. In real computers, erasure of bit register decreases information entropy by kln 2 and increases thermodynamic entropy (by HW-specific amount) associated with the register. These are two different kinds of entropies.
In short, real world energy costs are far higher than Landauer's limit due to current tech limitations, and possible energy cost savings in the future aren't hard limited by Landauer's limit at all. Landauer's idea is simply too problematic. Don't rely on it for any argument about real world.
Finally, don't learn physics from computer science guys, even if their name is Bruce Schneier. Just as you wouldn't learn computer science from physics experts.
No, that is a restatement of the First law of thermodynamics. Second law states that it is impossible to systematically (cyclically) extract heat and turn it completely into equivalent amount of work.
The record for lowest temperature is 1e-10 Kelvin and there is no theoretical limit as to how many zeroes can be added. So there is no hard limit, given good enough cooling/thermal isolation, the energy cost can be brought down. In theory, it can be brought down to zero.
> To run a computer cooler than that would require a heat pump, which means adding additional energy to the system than what is needed for our computation.
Sometimes the speed-up is a little, sometimes it is a lot.