  The mutual information method has demonstrated to be very useful for deriving
the potential order parameter of a system. Although the method suggests some
constraints which help to define this quantity, there is still some freedom in
the definition. The method then results inefficient for cases where we have
order parameters with a large number of constants in the expansion, which
happens when we have many degenerate vacuums. Here we introduce some additional
constraints based on the existence of broken symmetries, which help us to
reduce the arbitrariness in the definitions of the order parameter in the
proposed mutual information method.
