Renormalization symmetry and the Legendre transformation are imposed on a parametized
form of ergodic source uncertainty, a widely-applied model for “languages” ranging from the
spoken word to genetic codes. Using the Shannon–McMillan theorem to identify a duality
between source uncertainty and free energy density, this procedure:(i) suggests that a
punctuated “phase change” and resulting sudden fragmentation or coalescence should be
the norm for “language”-based phenomena, particularly the transfer of “genetic” information …