  This article focuses on a preaveraging description of polymer nonequilibrium
stretching, where a single polymer undergoes a transient process from
equilibrium to nonequilibrium steady state by pulling one chain end. The
preaveraging method combined with mode analysis reduces the original Langevin
equation to a simplified form for both a stretched steady state and an
equilibrium state, even in the presence of self-avoiding repulsive interactions
spanning a long range. However, the transient stretching process exhibits
evolution of a hierarchal regime structure, which means a qualitative temporal
change in probabilistic distributions assumed in preaveraging. We investigate
the preaveraging method for evolution of the regime structure with
consideration of the nonequilibrium work relations and deviations from the
fluctuation-dissipation relation.
