Abstract
Recent advances in non-equilibrium statistical mechanics and single-molecule measurements have enabled the determination of equilibrium free energies from non-equilibrium work measurements for fluctuating systems ranging from biological molecules to quantum oscillators. However, for many important non-equilibrium processes, it is difficult or impossible to apply and measure the work required to drive the system through the relevant conformational changes. Here, we show that it is possible, with an appropriate extrapolation to infinite temporal scale and zero spatial scale, to determine equilibrium free energies, without work measurement, by analysing the stochastic trajectories of single biomolecules or other nanoscale, fluctuating systems as they spontaneously relax from a non-equilibrium initial state. We validate the method with simulations and demonstrate its application by determining the free-energy profile for DNA molecules in a structured nanofluidic environment with an experimental protocol that mimics many natural processes with energy injection followed by thermal relaxation.
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