A generalization of the generalized Langevin equation (GLE), the so-called irreversible GLE (iGLE) [Hernandez, R.; Somer, F. L. J. Phys. Chem. 1999, 103, 1064], is further extended to describe non-stationary environments in which the non-stationarity is induced by the macroscopic behavior of the ensemble itself, rather than an external force. Such a formalism lends itself to the dynamical study of the length distributions of growing polymers.