Can Laplace's formula model a deterministic universe that is irreducibly probabilistic?

If we assume the Thesis that any classical Turing machine T, which halts on every n-ary sequence of natural numbers as input in a determinate time t(n), determines a PA-provable formula, whose standard interpretation is an n-ary arithmetical relation f(x1, …, xn) that holds if, and only if, T halts, then we can define Laplace’s formula recursively such that it can model the state of a deterministic quantum universe that is irreducibly probabilistic.