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 d W / d t = ∂ H ( x , t ) / ∂ 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.