From what I gather (and please correct me if I'm wrong), Jaynes argues that thermodynamic and information entropy are the same since the assumption in statistical thermodynamics that the energy distribution attained is that which maximizes the ways energy is distributed is equivalent to assuming the maximum ignorance distribution, which appears to me to be a subjective concept or at least one relating to information.
However, isn't this similarity just a coincidence? There are physical reasons energy maximizes the ways it is distributed (2nd law) having nothing to do with the fact that the distribution it attains happens to maximize our inability to describe the energy (maximizes ignorance). .
(Here I am talking about classical physics. I realize the uncertainty principle may unite information and thermodynamics in quantum.)
Update: The discussion in the link below has some claim that information and thermodynamic entropy are independent specific examples of a more general concept, but they are not equivalent.