One common method for proving that a data structure supports an operation in $O(f(n))$ amortized time is to construct a potential function $\Phi: \mathcal S \rightarrow \mathbf R^{+}$, which associates every state of the data structure with a positive real number, such that for any operation $\Delta \Phi + \text{actual time} = O(f(n))$.

Is the converse true, i.e. that for any data structure in amortized time $O(f(n))$ there is a potential function $\Phi$ which witnesses this fact (and has this amortized-time property) ? If not, are there are any non-artifical counterexamples?