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The rocky road from non-equilibrium work to free energy

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Although a few of very promising methods now exist for extracting free energy profiles of a many-body system from non-equilibrium work performed on it the implementation of these methods have proven to be non-trivial. These methods (most notable of all the Jarzynski equality the FR method and the Brownian dynamic FDT) typically require a proper sampling of the work performed on the system along many trajectories in the available phase space that connect the desired initial and final macrostates. One requires a transparent way of sampling the work performed on the system along each trajectory and then to assign residual work values to each 'bin' along the range under study. This becomes a seemingly arbitrary process when done along steered molecular dynamics trajectories. As a result of Brownian motions the system will repeatedly pass back and forth the boundaries of each bin along the reaction path and proper sampling of non-equilibrium work becomes challenging.A method for measuring non-equilibrium work in such cases will be presented with discussions on error analysis and how to address the issue of correlations among adjacent samplings of work for each bin. Applications of this method to a test system and also to a couple of peptide-membrane systems will be presented and discussed as well as the relative reliability of the results based on theoretical arguments and the agreement among different methods.