A generalization of the generalized Langevin equation (stochastic dynamics) is introduced in order to model chemical reactions which take place in changing environments. The friction kernel representing the solvent response is given a non-stationary form with respect to which the instantaneous random solvent force satisfies a natural generalization of the fluctuation-dissipation relation. Theoretical considerations, as well as numerical simulations, show that the dynamics of this construction satisfy the equipartition theorem beyond its equilibrium limits.

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.

A generalization of the generalized Langevin equation (stochastic dynamics) is introduced in order to model chemical reactions which take place in environments with both density and temperature variations. This phenomenological constructionsgiven the name irreversible generalized Langevin equation (iGLE)sensures that both the bath and its response to the chosen coordinates of the projected systems are characterized by the same imposed temperature profile. As in the earlier construction, the present generalization does reproduce the generalized Langevin equation in equilibrium and quasi-equilibrium limits. Numerical results indicate surprising behavior when the temperature ramping conditions are fast compared to the solvent response.

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