Why would you have that as a requirement? Output shouldn't vary unless input does. Real world physics only vary because input conditions are never the same.
It's my impression that it's always easier to add randomness to such an engine. So if you have a deterministic engine you can always sprinkle on some randomness afterwards if you want it more interesting.
But I'm not very experienced in physics engines so I might be on thin ground.
>Real world physics only vary because input conditions are never the same.
Not exactly. Classical physics is a deterministic approximation of quantum physics at macro scales. In reality, outcomes vary even if the initial conditions are the same (although you may need special equipment to observe that there is any difference. You can choose to call all of the quantum events "inputs" but that's dodging the point.
That said, most applications would not benefit from simulating at a quantum level, and doing so at large scales is currently intractable. So while real world physics is not deterministic, macro scale physics engines should be.
It's my impression that it's always easier to add randomness to such an engine. So if you have a deterministic engine you can always sprinkle on some randomness afterwards if you want it more interesting.
But I'm not very experienced in physics engines so I might be on thin ground.