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I've found similar threads like this, but with no clear answer. I understand that the specific heat capacity of a substance increases with temperature, because the vibrational nodes and rotational movements of the atoms are quantized (I assume that the increase is because the energy is distributed evenly over all degrees of freedom?).

What I don't understand is why the heat capacity goes to zero as temperature goes to zero. This comes out of the mathematics, sure - but what is the physical explanation here? If the translational movements are not quantized (or temperature-dependent, rather), what is explanation?

I hope my question makes sense.

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Short answer: at absolute zero there is one - and only one - energy state available to each particle. Any attempt to change the state of even a single particle introduces energy into the system and you're no longer at absolute zero. Put another way: if there were two energy states allowed for a particle, the number of available energy states would be N for N particles (any one of them might be in the second state), and the temperature, which is proportional to the logarithm of the number of available states, is greater than zero.

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  • $\begingroup$ Can't you have configurations where there a locked in entropy at 0? for example a system with two particles of spin up and one particle of spin down. en.m.wikipedia.org/wiki/Residual_entropy $\endgroup$
    – Viktor
    Commented Oct 15, 2015 at 16:49
  • $\begingroup$ @Viktor That article, I think, refers to relative entropy of glass vs crystalline configuration, but the glass cannot collapse further. So far as I can tell, and I could very well be wrong, you still can't apply heat to the glass without forcing it above zero Kelvin. $\endgroup$
    – Carl Witthoft
    Commented Oct 15, 2015 at 19:37
  • $\begingroup$ Thanks for your answer. I have expanded my question below :) $\endgroup$
    – user95642
    Commented Oct 17, 2015 at 11:30

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