Information Theory, Scaling Laws and the Thermodynamics of Evolution

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 within reproducing populations; (ii) gives a power law for that phase change near transition; (iii) provides a "disorder" construct similar to an entropy which may trigger higher degrees of punctuation in social systems than is suggested from simple physical analogs; and (iv) gives "equations of state" relating ensemble averages which should be observable within coalesced systems. The general formalism is explicitly applied to problems of speciation, coevolution and group selection, and comparison made with the work of Eigen and his associates.Copyright 1998 Academic Press Limited