Determining Pathways of Minimum Work: Simple Examples

The calculations of minimal work pathways (MWP) are considered. These pathways are useful for efficient free energy calculations and in designing Candidate Monte Carlo Moves, which enables efficient sampling of rough landscapes (Nilmeier, J. P.; Crooks, G. E.; Minh, D. D. L.; Chodera, J. D., Nonequilibrium candidate Monte Carlo is an efficient tool for equilibrium simulation. Proc. Natl. Acad Sci. USA 2011, 108 (45), E1009-E1018). We describe an approach for a grid search of MWP. The approach assumes that the parameter space is smooth and is presented accurately on a coarse mesh. Three examples are discussed: Two examples of 2-dimensional landscapes and an example of a mutation of a Lennard Jones sphere. In two examples, we identify MWP at fixed short times. The third example has a broad funnel of minimal work pathways without a clear MWP.