The irreversible generalized Langevin equation (iGLE) contains a nonstationary friction kernel that in certain limits reduces to the GLE with space-dependent friction. For more general forms of the friction kernel, the iGLE was previously shown to be the projection of a mechanical system with a time-dependent Hamiltonian. [R. Hernandez, J. Chem. Phys. 110, 7701 (1999)] In the present work, the corresponding open Hamiltonian system is further explored. Numerical simulations of this mechanical system illustrate that the time dependence of the observed total energy and the correlations of the solvent force are in precise agreement with the projected iGLE.

A three-dimensional model for polymerization processes in nonequilibrium environments has been constructed as an extension of an earlier two-dimensional polymer-growth-Hamiltonian model [M. Vogt and R. Hernandez, J. Chem. Phys. 115, 1575 (2001)]. The extension to three dimensions will permit a direct comparison with experiments, and presently allows us to observe the effects of reduced conformational trapping as one scales from two to three dimensions. The three-dimensional model exhibits surprisingly similar equilibrium and dynamic behavior to the two-dimensional model with the exception that it grows large polymers which are more compact. The radius of gyration scales weaker with the polymer size in three dimensions as has been seen in other models. The effects of temperature ramping and jumps on the dynamics of cross-polymerization have also been examined and exhibit a switch over from linear to nonlinear response for larger perturbations.

A polymer growth Hamiltonian with an accompanying novel lattice has been constructed to model reaction dynamics of polydisperse polymer systems that have kinetics affected by an environment which is altered over time by the polymerization process itself. Monte Carlo dynamics are used to simulate the polymerization process with bond breaking/formation moves analogous to a correlated percolation model. Lattice events thus occur on the time scale of reactivity rather than the much shorter time scales of either monomer motion or conformational dynamics, though an effort is made to include the latter as well. The equilibrium behavior of the system has been well mapped out and is complex enough to model a variety of real polymer systems such as solid state polymerization, living polymers and thermosetting polymers. Detailed equilibrium structural information such as molecular weight distributions and extent of cross polymerization have been obtained. Pseudodynamic information such as the time-dependence in the polymer weight distribution and more detailed quantities may also be obtained with respect to Monte Carlo time scales.