I was reading a paper of E.T. Jaynes 'Information Theory and Statistical Mechanics'. There he mentions the following principle in the section 'Application to Statistical Mechanics':
" There is nothing in the general laws of motion that can provide us with any additional information about the state of system beyond what we have obtained from measurement "
then he goes on to discuss an consequence of this principle in the next paragraph where a supermathematician has discovered a new integral of motion. He goes on to say that it is expected that this would change the resulting form of equations and that additional experimental data regarding these constants would help avoid a similar problem in prediction problem.
Then he describes the consequence in terms of metric transitivity and phase space.
So what is the role of metric transitivity in statistical mechanics and what role does it have in this particular context of having another uniform integral of motion.