The inequality –${\sum }_1^n{p}_i\text{log}{p}_i\le –{\sum }_1^n{p}_i\text{log}{q}_i$ where (p₁,…, p_n) and (q₁,…,q_n) are probability distributions, with equality if and only if p_i = q_i for all i. The inequality is important in information theory. See also entropy (Shannon entropy).