> The only part of your statement that is still probabilistic is "entropy will not decrease" The markov/IT version of the 2nd law is a statement about macrosta

> The only part of your statement that is still probabilistic is "entropy will not decrease" The markov/IT version of the 2nd law is a statement about macrostate entropy (taking the entire microstate ensemble for each macrostate), and in that sense it is not probabilistic. See the Cover&Thomas reference I gave earlier for the exact definition. It is indeed different than how it is usually taught in physics, in which the microstates are differentiated. I guess we both need to be more careful about mathematical definitions in the future ...