This is a bit of a shower-thought, so forgive me if it is ill-conceived or a stupid question!
It occurred to me that, to preserve information, you need to use energy. For example, say you have a book -- as a lay encapsulation of information -- energy is required both to create that book and then maintain its contents: Energy is converted to information.
From the other perspective, anything with structure could be thought of as having an information content. This is perhaps a bit of a philosophical argument, but a lump of coal is a lump of coal by virtue of its structure. If you chemically destroy that structure, you get heat (and no coal). That is, information is converted to energy.
So my proposition is that information is a function of energy (and vice versa). Say:
Presuming this is not a flight of fancy:
- Is this function $k$ known or studied (presumably where "information" is quantified in the context of Shannon Information Theory, rather than "books", etc.)?
- Can a coherent narrative be made -- something that is broadly understandable -- that relates information to, say, $mc^2$, without making my above argument?
- At what point does my book example become zero-sum (i.e., the information contained in something balances the entropy incured to create and maintain it)?
- Are there instances where it makes sense to think of things in terms of information content, as opposed to energy (or related units)?