Ralph's equivalent circuit model, revised Deutsch's maximum entropy rule and discontinuous quantum evolutions in D-CTCs

We examine Ralph’s equivalent circuit model of D-CTCs, which was proposed to derive Deutsch’s maximum entropy rule of D-CTCs. By constructing counterexamples we show that the equivalent circuit model does not always reproduce the unique fixed state with the maximal von Neumann entropy. We speculate that the equivalent circuit model remains the correct description of D-CTCs and it can reproduce a revised maximum entropy rule of D-CTCs. We also suggest that the revised maximum entropy rule may eliminate the discontinuous quantum evolutions of D-CTCs.