Reversibility and efficiency in coding protein information

We examine the codes for the distributions of amino acids that exist in nature and show that they could not be both time efficient and reversible. We investigate a family of Zipf-type distributions and present their efficient (non-fixed length) prefix code, their graphs, and the condition for their reversibility. We prove that for a large family of such distributions, if the code is time efficient, it could not be reversible. In other words, if pre-biotic processes demand reversibility, the protein code could not be time efficient. The benefits of reversibility are clear: reversible processes are adiabatic, namely, they dissipate a very small amount of energy. Such processes must be done slowly enough; therefore time efficiency is non-important. It is reasonable to assume that early biochemical complexes were more prone towards energy efficiency, where forward and backward processes were almost symmetrical.