I am curious about the relationship between energy and information. I have only a beginner's knowledge, having read Shannon's original paper and a little about Landauer's limit which states that the minimum amount of energy required to erase 1 bit of information is about 0.0175 eV (a tiny amount, about 1/10 the current upper bound on the sum of rest energies of neutrinos, 0.120 eV).
A thought experiment: given some object (say, a plastic model of a komodo dragon), if we take a digital photo in a pitch black environment, the CCD sensors will read out an array of 0's. Using Kolmogorov's definition of information, this is highly compressible and will be a small amount of info. On the other hand, if we turn up the power of a light bulb and make it extremely bright, the data will be all 1's, which is also highly compressible. However, somewhere in the middle, there will be a picture of a komodo dragon which isn't very compressible, and so will contain more information. If we vary the brightness continuously, and average over many different objects, we expect a smoothly varying concave function which peaks somewhere in the middle. Normalizing with zero brightness 0 and maximum brightness 1, we might guess the peak occurs at 1/2.
I downloaded a camera app (Manual Camera) on my phone that allows one to manually change the exposure settings (aperture, ISO, & shutter speed), and tested this out by keeping the light constant and changing one of them over 25 gradations and used about 15 different objects. The full dataset is ~500mb so difficult to make publicly available. Since .jpeg is already a compression algorithm, I take the filesize to be an approximation of K-complexity. The resulting plot is attached (x-axis are the 25 brightness settings, y-axis is filesize in bits).
Q1: Can this be modeled mathematically/physically, and in the resulting model where should the peak occur for a generic object?
Q2: If this is too difficult, are there any good papers exploring the relationship between energy and information?
Have a look on: Elements of Information Theory Thomas M. Cover Joy A. Thomas
and https://physics.stackexchange.com/questions/22084/how-is-information-related-to-energy-in-physics