  We study information theoretic quantities in models with three and four spin
interactions. These models show distinctive characteristics compared to their
nearest neighbour counterparts. Here, we quantify these in terms of the Nielsen
complexity in static and quench scenarios, the Fubini-Study complexity, and the
entanglement entropy. The models that we study have a rich phase structure, and
we show how the difference in the nature of phase transitions in these,
compared to ones with nearest neighbour interactions, result in different
behaviour of information theoretic quantities, from ones known in the
literature. For example, the derivative of the Nielsen complexity does not
diverge but shows a discontinuity near continuous phase transitions, and the
Fubini-Study complexity may be regular and continuous across such transitions.
The entanglement entropy shows a novel discontinuity both at first and second
order quantum phase transitions. We also study multiple quench scenarios in
these models and contrast these with quenches in the transverse XY model.
