Dear Steven Sax,
I found your essay the most careful and complete study of the nature of information [the topic of this contest] of the hundred I've read.
You mentioned "the merging of Shannon's information entropy and physical entropy...", But Jaynes, the first (in 1957) to show the utility of Shannon's theory for statistical mechanics, states that Shannon entropy is a probability (math) while physical entropy is based on energy (physics). You seem to keep this distinction well in mind: "entropy... derived from heat engines... unavailability of energy" while the second law is "statistical ... probability based cause" of entropy increase.
In my essay and elsewhere I note that 'information' as transferred is energy. Only when the energy crosses a threshold and transforms a structure ("in-forms" the structure) does the energy produce (stored) information. The bit is not a fundamental physical entity. It is the twofold nature of the threshold that is represented by the bit. The physical effects, if any, involve interpretation of the stored information, bringing consciousness or consciously designed systems into play.
For example, you note that Maxwell's demon "detects the molecule". It measures the energy and compares it to a threshold energy/temperature (via velocity measurement). This comparison yields the information used by the demon. Similarly the "coded information" in DNA is structural, being deposited when chemical thresholds link the next base to the chain. In general, you do an excellent job of not confusing energy and information.
I very much like your question "could emergent systems operate like components in a circuit, like local entities to create information [producing] greater entropic potential...?"
You also note Bekenstein's "entropy increase resulting from info" in the black hole and state: "This area (geometry) to information connection is fundamental." This is the conventional wisdom but I would suggest that exactly the same area relation arises from strictly energy considerations, where information never enters the picture. The info-to-area connection may or may not be fundamental. However your relating this to a statistics/area relation is fascinating, as is your mention of bridging statistics and geometry. I would be interested in your expanding on this theme. You present a more convincing argument for an info/area relation than most I've seen.
You then note that it is physical reality, not information per se, that directly affects things, with an example of "affect structure in an atom."
Finally you present entanglement questions about information that are too complex for me to comment on. But you do an excellent job analyzing these.
By far the best analysis of the reality of information I've seen. Congratulations and thanks.
I hope you find the time to read my essay and comment.
Best regards,
Edwin Eugene Klingman