I am trying to understand the connection between the entropy in Thermodynamics vs. entropy in Information Theory and I think a good way to clarify/illustrate it would be to find an analogy of microstates and macrostates within Shannon's definition of entropy. If thermodynamic entropy is based on the 'ignorance' of microstates given a macrostate and the information entropy is based on the 'ignorance' of the message to be received in a given channel, what would correspond to micro- and macrostates in this communication channel? I know these are terms defined in thermodynamics, but since the equations are more and less the same, it appears to me that there should be analogies in information theory and that could be useful to compare these two definitions/contexts of entropy.
EDIT: After some further reading I put up the following table, however I am not sure if I'm doing it right:
╔══════════════════════════╦═══════════════════════════╗ ║ THERMODYNAMICS ║ INFORMATION THEORY ║ ╠══════════════════════════╬═══════════════════════════╣ ║ Phase-space ║ Alphabet (sign set) ║ ║ ║ + occurance ║ ╠══════════════════════════╬═══════════════════════════╣ ║ Micro-states: ║ Occurance of signs picked ║ ║ location of particles ║ from the alphabet ║ ║ in the phase-space ║ ║ ╠══════════════════════════╬═══════════════════════════╣ ║ Macro-states: ║ Probability distribution ║ ║ Probability distribution ║ of symbols to be picked ║ ║ of particles to be found ║ from the alphabet ║ ║ in bin B ║ (or to occur) ║ ╠══════════════════════════╬═══════════════════════════╣ ║ Bin in the distribution: ║ Bin in the distribution: ║ ║ Quantized phase-space ║ Symbol in the alphabet ║ ║ location ║ ║ ╚══════════════════════════╩═══════════════════════════╝