I just noticed a paper that Carlo Rovelli wrote on the 2nd law of thermodynamics. He is a physicist famous for quantum gravity, and usually has interesting things to say, but he seems to not have read Stephen Wolfram's A New Kind of Science. He makes a conjecture that complex systems always admit a coarse-graining where entropy is monotonic, but if he'd just look at section 9.3 he would've benefited from Wolfram's observations. Among them is the reversible rule 37R, which is most easily implemented as a four color rule, which is definitely complex and definitely not monotonic in any sense.

ArrayPlot[Mod[CellularAutomaton[{339044861442636834121823371987194788625, 4, 1}, ArrayPad[RandomInteger[1,20],50], 1000],2]]

Wolfram's book has a longer picture on p.454 which shows order followed by a mess and then it becomes more ordered, and so on.