Failure of the work-Hamiltonian connection for free-energy calculations

Extensions of statistical mechanics are routinely being used to infer free energies from the work performed over single-molecule nonequilibrium trajectories. A key element of this approach is the ubiquitous expression dW/dt=partial derivative H(x,t)/partial derivative t, which connects the microscopic work W performed by a time-dependent force on the coordinate x with the corresponding Hamiltonian H(x,t) at time t. Here we show that this connection, as pivotal as it is, cannot be used to estimate free-energy changes. We discuss the implications of this result for single-molecule experiments and atomistic molecular simulations and point out possible avenues to overcome these limitations.