What I'm doing here is beginning to dig into the relationship between entropy and information as it applies to replication in earliest life. Based on my amateur and sparsely read understanding, the cost in energy of adding a specific monomer out of a group of potential monomers to a growing polymer should be much higher than that of adding a random monomer.
For the moment I'm going to leave it at that, adding further as comments as they become appropriate. Any comments that help improve understanding of this subject will be very welcome.
Note: I'm not going to allow this thread to devolve into a debate over creationism of any sort (including "ID").
Links to Relevant Papers (Abstracts only where I couldn't find full texts.)
Shannon entropy applied from panda's thumb
Entropy and Information Theory by Robert M. Gray
Evolution of Biological Information by Thomas D. Schneider
Evolved RNA Secondary Structure and the Rooting of the Universal Tree of Life by Gustavo Caetano-Anollés
Life's Emergence is Not an Axiom: A Reply to Yockey by Avshalom C. Elitzur
About a Symmetry of the Genetic Code by A. J. Koch and J. Lehmann
Self-organization vs. self-ordering events in life-origin models by David L. Abela, and Jack T. Trevors
Global similarities in nucleotide base composition among disparate functional classes of single-stranded RNA imply adaptive evolutionary convergence. by E Schultes, Hraber, and T H LaBean
Evolution in thermodynamic perspective: An ecological approach by Bruce H. Weber, David J. Depew, C. Dyke, Stanley N. Salthe, Eric D. Schneider, Robert E. Ulanowicz and Jeffrey S. Wicken
The Origin and Evolution of tRNA Inferred from Phylogenetic Analysis of Structure by Feng-Jie Sun and Gustavo Caetano-Anollés
MODELLING AND GENERATING COMPLEX EMERGENT BEHAVIOUR by Kirsty Kitto
Causation and the Origin of Life. Metabolism or Replication First? by Addy Pross
The Driving Force for Life’s Emergence: Kinetic and Thermodynamic Considerations by Addy Pross
On the Emergence of Biological Complexity: Life as a Kinetic State of Matter by Addy Pross
Thermodynamics, information and life revisited, Part I: To be or entropy by Peter A. Corning, Stephen Jay Kline
Thermodynamics, information and life revisited, Part II: Thermoeconomics and Control information by Peter A. Corning, Stephen J. Kline
Modeling the Emergence of Complexity: Complex Systems, the Origin of Life and Interactive On-Line Art by Christa Sommerer and Laurent Mignonneau
What is complexity? by Christoph Adami
Does complexity always increase during major evolutionary transitions? by Mercedes Bleda-Maza de Lizana, Hannelore Brandt, Ille C. Gebeshuber, Michael MacPherson, Tetsuya Matsuguchi, and Szabolcs Számadó
I'll add further links in subsequent comments as I find them, so this post can be left unchanged.