Information theory, scaling laws and the thermodynamics of evolution

Abstract

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.