The entropy has the property that S ( X ) ≤ ≤ S ( Y ) if and only if X ≺ ≺ Y and S ( X ) = S ( Y ) if and only if X ∼ ∼ A Y in accord with the Second Law. If we choose two states X 0 and X 1 such that X 0 ≺ ≺ X 1 and assign entropies 0 and 1 respectively to them, then the entropy of a state X where X 0 ≺ ≺ X ≺ ≺ X 1 is defined as: