H c is the negative of the Kullback–Leibler divergence, or discrimination information, of m (x) from p (x), where m (x) is a prior invariant measure for the variable(s). The relative entropy H c is always less than zero, and can be thought of as (the negative of) the number of bits of uncertainty lost by fixing on p (x) rather than m (x). Unlike the Shannon entropy, the relative entropy H c has the advantage of remaining finite and well-defined for continuous x, and invariant under 1-to-1 coordinate transformations. The two expressions coincide for discrete probability distributions, if one can make the assumption that m (x i) is uniform – i.e. the principle of equal a-priori probability, which underlies statistical thermodynamics.