Surprise = 0 seems to be naturally tied to the concept of omnipotence and omnipresence - intuitive and conceptually graspable, though there seems to be a glaring question whether an experience can exist under such conditions. But maximum complexity is another animal to consider - does such complexity have an upper bound? Would modeling maximum complexity be achieved only through a reduced, compressed representation, or is it achievable to represent such unpacked in all it's glory? How could this be without establishing boundaries? Maybe we need to reconsider the units in which the integral is under evaluation -- say, 0 --> inf translates to something more functional. The mathematical equivalent of transforming a noun to a verb - a value to a function. The integral evaluated across the bounds of a function - and yet the function itself becomes recursive. So I suppose at the nth degree, this maximum complexity can be evaluated, with the "contingency" that the result of the maximum will yield a recursive comparator.
Another thing to supplement this idea is to consider the following: what would it mean to reach maximum complexity? How could it be, to arrive at a truly finite limit of complexity? Nature would always find a way to expand expression through transformation. Likewise, nature favors simplification, reductionism - an over drive for efficiency as this opens the door to introduce further complexity. A dance of complex order.
This seems far more logically consistent than stagnation - change is necessary for measure. And detection is necessary for experience. Thus, without such dynamics (even if considering the dynamics of parts within an unchanging whole), there is nothing to consider. A change in direction, dismantling that which is of less use to free resources for use towards that of more value - that which creates order at a higher degree of freedom. Of course, "freeing resources" is a narrative associated with the action, driven by governing dynamics and relational patterns. A narrative driven association being useful nonetheless, as these associations add complex layers so long as such are stored temporarily - a note for another entry.