Boltzmann Equation for Entropy:
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It is the only entropy that is left after you take out all types of entropy like thermal entropy. When you reduce the temperature and try to get to 0 Kelvin, the molecules would not be in motion. The only entropy that would be left is the positional entropy. One molecule could be in multiple orientations and that is the residual entropy. If it is a perfect crystal and is only in one, perfectly ordered position, the entropy would be 0. But this isn't the case for many molecules so there is some entropy.
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