  The idea of fractional exclusion statistics proposed by Haldane is applied to
systems with internal degrees of freedom, and its thermodynamics is examined.
In case of one dimension, various bulk quantities calculated show that the
critical behavior of such systems can be described by $c=1$ conformal field
theories and conformal weights are completely characterized by statistical
interactions. It is also found that statistical interactions have intimate
relationship with a topological order matrix in Chern-Simons theory for the
fractional quantum Hall effect.
