Jaynes' book circulated for a while on the internet in draft form, and a number of chapters never made it to the final published version. One of those was a generalization of maximum entropy to dynamic systems, where he called the thing to be maximized guage, I believe. I think it was an exponential raised to a matrix, but it's pretty hazy for me at this point.

Did anything ever come of that?

I thought I saw a paper discussing it a while ago, published maybe around 2007.