  With the traditional equilibrium molecular simulations, it is usually
difficult to efficiently visit the whole conformational space in complex
systems, which are separated into some metastable conformational regions by
high free energy barriers. The applied non-equilibrium process in simulations
could enhance the transitions among these conformational regions, and the
associated non-equilibrium effects can be removed by employing the Jarzynski
equality (JE), then the global equilibrium distribution can be reproduced.
However, the original JE requires the initial distribution of the
non-equilibrium process is equilibrium, which largely limits the application of
the non-equilibrium method in equilibrium sampling. By extending the previous
method, the reweighted ensemble dynamics (RED), which re-weights many
equilibrium simulation trajectories from arbitrary initial distribution to
reproduce the global equilibrium, to non-equilibrium simulations, we present a
method, named as re-weighted non-equilibrium ensemble dynamics (RNED), to
generalize the JE in the non-equilibrium trajectories started from an arbitrary
initial distribution, thus provide an efficient method to reproduce the
equilibrium distribution based on multiple independent (short) non-equilibrium
trajectories. We have illustrated the validity of the RNED in a one-dimensional
toy model and in a Lennard-Jones system to detect the liquid-solid phase
coexistence.
