The diagonal entropy was introduced as a good entropy candidate especially
for isolated quantum systems out of equilibrium. Here we present an analytical
calculation of the average diagonal entropy for systems undergoing unitary
evolution and an external perturbation in the form of a cyclic quench. We
compare our analytical findings with numerical simulations of various many-body
quantum systems. Our calculations elucidate various heuristic relations
proposed recently in the literature.Comment: 5 pages + 4 page "Supplemental material", 2 figure
