Before revision:  We prove  the non-equivalence with a counterexample that exhibits a Markov blanket but does not satisfy the rewritten equations. Our counterexample also invalidates the corresponding (but more general) rewritten equations in the more recent Friston (2019). The second error concerns the Free Energy Lemma itself, which we prove, by counterexample, to be wrongin general. The third is the claim that the Free Energy Lemma , when it does hold, implies equality of variational density and ergodic conditional density.
After revision:  We prove the original free energy lemma, when taken at face value, is wrong. We show further that this free energy lemma , when it does hold, implies equality of variational density and ergodic conditional density.