Relative entropy is directly related to the Fisher information metric. This can be made explicit as follows. Assume that the probability distributions P and Q are both parameterized by some (possibly multi-dimensional) parameter θ θ . Consider then two close by values of P = P ( θ θ ) and Q = P ( θ θ 0 ) so that the parameter θ θ differs by only a small amount from the parameter value θ θ 0 . Specifically, up to first order one has (using the Einstein summation convention)