Steady State Free Energy Landscape in Non-Equilibrium and Equilibrium Conditions

The growing global demand for water, the imperative to reduce harmful gas production, and the need for low energy consumption have underscored the importance of engineering highly functionalized membranes for efficient separation processes. However, conventional molecular dynamics simulations often fall short of capturing rare events within feasible timescales. To address this challenge, we developed a novel method to construct free energy profiles using non-equilibrium sampling of predefined initial and final states in both equilibrium and non-equilibrium systems. This innovative approach involves tracking a tracer particle amidst a collection of simulations launched at different inter-phases, without prior knowledge of the underlying free energy landscape. The trajectory data obtained from these simulations are utilized to construct a transition matrix, which enables the extraction of the free energy profile through the steady-state probability distribution. The key eigenvalue associated with the transition matrix corresponds to the eigenvector that characterizes the steady-state probability distribution. This novel method holds tremendous potential across various engineering applications, including the design of materials in the battery industry, the development of nano-filtration membranes, and the exploration of host-guest systems.