I recently read a paper from the year 1965, and in the paper, the authors proved that there is no general function way to maximize or minimize the production rate of entropy. (Gage et al. 1965 "The Non-Existence of a General Thermokinetic Variational Principle.")
I think that this is an important statement.
Around the same time in the 1960s, there were "proofs" for both maximization and minimization of the entropy production rate, dS(irr)/dt. While either of these case can be true near equilibrium given certain constraints, these "principles" are not true in general.
So, I just want to follow up on the previous blog by stating that, while the entropy of the universe is increasing, it is not following the "fast possible route." There is no way to predict the future, so how can we ever know that a local increase of the entropy rate could ultimately cause a large slow down in the entropy rate globally.
What if a large explosion was set off locally? (this would cause a rapid increase in the entropy production rate.) However, if this explosion were due to a nuclear weapon, then it could cause a global problem for all life, which would cause the entropy production rate to decrease.
And here's the ultimate problem with "principles of max/min entropy production rate" : the principle is not valid far-from-equilibrium under non-steady-state conditions, but that's exactly where we live. We live on planet that is far-from-equilibrium (if equilibrium is taken to be the ~3 degrees Kelvin vacuum that is most of space, and could ultimately be all of space.)
So, in conclusion, be careful if you ever run into a paper that proves that the entropy of the universe is increasing at its maximum (or minimum) possible route.
All we can say is that the entropy production rate on the Earth is faster than if life were not here. We can not prove that the actions we are taking this very moment are in fact causing the fastest possible rate of entropy production.