Residual entropy of ice: A manifestation of the fractional exclusion statistics in real three-dimensional space

We report here a tangible example of the fractional exclusion statistics in three spatial dimensions. We identify the chemical constraint of O-H bonds in ice, the so-called ice rule, as the origin of this novel statistics. Then the residual entropy of the crystalline ice is recognized as arising from the fractional exclusion with the statistical interaction parameter alpha = 0.867. Assuming the residual entropy of ice reflects true accessibility to a macroscopic number of states through quantum tunnelling, we propose the possibility that Berry's phase suppresses the tunnelling splitting of ground states and maintains the finite residual entropy.