The entropy of such a system which is at absolute zero must be identically zero.
You would have a hard time reaching absolute zero.
Even if it is possible, it's difficult to maintain it.
As derived by Max Planck from ideas of Nerst's Heat theorem, the entropy of a system, reversible or otherwise is constant at absolute zero and can be taken to be zero at that temperature.
A zero entropy state corresponds to perfect order, since entropy is a measure of the disorder of the system.
Then all pure atoms would collapse to the most ordered zero entropy state (zero motion), and all molecules would only be vibrating (stretching and bending) without flying around and rotating.
Note: at zero ground state temperature, the quantum fluctuations are large in comparison to the energy available, and make it hard for a state to be localised. This is one possible explanation to why one cannot easily maintain absolute zero.