On the work - Hamiltonian connection in manipulated systems

I examine the 'physical inconsistencies' pointed out in a recent work as deriving from the use of the expression dW/dt = ?H(x, t)/?t which appears in fluctuation relations for manipulated system, such as Jarzynski's equality. I show that these inconsistencies are illusory, since the 'arbitrary parameters' that appear in the expression of the free-energy difference obtained from this relation turn out to have a direct and simple physical interpretation connected with the physical setup needed to perform the manipulation.