To my very limited understanding, no. Basic example, puring cream into a cup of coffee. At first low entropy, low complexity (cream at top, coffee at bottom).

To my very limited understanding, no. Basic example, puring cream into a cup of coffee. At first low entropy, low complexity (cream at top, coffee at bottom). Then higher entropy, high complexity (cream and coffee mix according to laws of physics, different concentrations at different locations in the cup, streams and such). At last, highest entropy but again low complexity (everything is homogenous).