Every realistic model of computation is polynomial time reducible to probabilistic Turing machines
Which amounts to saying that every computable process in the universe can be efficiently simulated by a probabilistic Turing machine.
The definition of realistic model appeals to intuition rather than a precise definition of realistic. A rule of thumb is that a computation model is realistic if it could be used to accurately model some physical process. For example, there is a clear relation between the model of register machines and the inner workings of personal computers. On the other hand, a computational model which can access an NP oracle does not have a physical counterpart.
As it happened with the standard Church-Turing thesis, this is an inductive rather than a mathematically defined statement. However, unlike the standard CT thesis, it is widely believed to be wrong, primarily because quantum computation stands as a highly likely counterexample to the thesis.
We remark that non-deterministic computation is not a candidate counterexample to the strong CT thesis, since it is not realistic. That said, we can find a relation between the two concepts: if and then , so quantum computation can be efficiently simulated, and we lose the strongest contestant for a counterexample to Strong CT.
The falsehood of the Strong CT thesis opens up the possibility of the existence of physical processes that, while computable, cannot be modeled in a reasonable time with a classical computer. One consequence of this, that would also mean that if quantum computing is possible the speed .up it provides is non-trivial.
Epistemic processes which assign priors using a penalty for computational time complexity are misguided if the Strong CT thesis is false. See for example Levin search.