ComputationalEntropyRate

Mechanism

Treat a channel as computational: it accepts or rejects inputs according to a language (a password validator, an environment selecting viable genomes, a colleague judging an idea). The computational entropy rate is the number of bits that must be submitted for each bit accepted; if 66% of submitted length is accepted, the rate is about 1.5. It looks like the friction of ChannelCapacity, but the cause is different: low Shannon capacity reflects meaningless noise, while a high computational entropy rate reflects meaningful rejection, i.e. the channel doing more work. The rate measures the difference in information between two languages, the generator's and the acceptor's. A further ratio, the computational channel flow ratio, compares the average length of accepted inputs with rejected ones: a channel that rejects short inputs early and accepts long ones can consider more options at the same entropy rate, as a writer who bins bad pages early can afford to be more critical.