Well, yes. Maximum information = Maximum randomness. This is why "modem sounds" are like white noise - both are maximum entropy. The probability of ANY state

Well, yes. Maximum information = Maximum randomness. This is why "modem sounds" are like white noise - both are maximum entropy. The probability of ANY state is maximized to the channel capacity. For binary words, that means every combination of bits would exist. That's not going to be as compressible as a situation with redundant bits or states. Maximum compression is also related to this: if you have maximum entropy, you have maximum compression and maximum channel capacity. You also have "most perfect encryption" if the data has been encrypted - again redundancy means encryption can be broken faster/easier than maximum entropy. All nicely related. All commonly dealt with in digital modulation and wireless technologies (I learned all this as an EE long before the digital communications revolution arrived - came in handy for sure).