If you know that every subfield of your state object is immutable, and you're using references instead of "local" copies (inconvenient unless you have garbage collection) then your copying costs are limited to the size of the overall state object plus whichever field changed.

Obviously this makes no sense for C++, but Clojure and OCaml get away with it and in Haskell it's the standard way of implementing almost every stateful computation.