Residual Entropy

Residual entropy is small amount of entropy which is present even after a substance is cooled arbitrarily close to absolute zero. It occurs if a material can exist in many different microscopic states when cooled to absolute zero. This can occur if it has many different ground states with exactly the same zero-point energy; it can also occur if the "ground states" have slightly different energies, but the system is prevented from finding and settling into the true lowest-energy state. It is seen most often in substances which have very weak tendencies to align into their energetic ground state, and/or which are cooled quickly.

A common example is the case of carbon monoxide, which has a very small dipole moment. As the carbon monoxide crystal is cooled to absolute zero, few of the carbon monoxide molecules have enough time to align themselves into a perfect crystal, (with all of the carbon monoxide molecules oriented in the same direction). Because of this, the crystal is locked into a state with different corresponding microstates, giving a residual entropy of, rather than zero.

Another example is any amorphous solid (glass). These have residual entropy, because the atom-by-atom microscopic structure can be arranged in a huge number of different ways across a macroscopic system.