Well, there is what is usually called quantum randomness. While many common kinds of randomness represent just lack of knowledge, contemporary physics says that quantum randomness (e.g. how much time will pass before a particular unstable atom decays) is different because it is impossible in principle to predict it. You can probably call it "utter lack of causality".

As to "idealized", I don't know. Depending on which framework you pick, the notions of "idealized randomness" might well differ.