  Complex systems are found in most branches of science. It is still argued how
to best quantify their complexity and to what end. One prominent measure of
complexity (the statistical complexity) has an operational meaning in terms of
the amount of resources needed to forecasting a system's behaviour. Another one
(the effective measure complexity, aka excess entropy) is a measure of mutual
information stored in the system proper. We show that for any given system the
two measures differ by the amount of information erased during forecasting. We
interpret the difference as inefficiency of a given model. We find a bound to
the ratio of the two measures defined as information-processing efficiency, in
analogy to the second law of thermodynamics. This new link between two
prominent measures of complexity provides a quantitative criterion for good
models of complex systems, namely those with little information erasure.
