Abstract
We recently showed that the dynamics of coarse-grained observables in systems out of thermal equilibrium are governed by the non-stationary generalized Langevin equation [H. Meyer, T. Voigtmann, and T. Schilling, J. Chem. Phys. 147, 214110 (2017); 150, 174118 (2019)]. The derivation we presented in these two articles was based on the assumption that the dynamics of the microscopic degrees of freedom were deterministic. Here, we extend the discussion to stochastic microscopic dynamics. The fact that the same form of the non-stationary generalized Langevin equation as derived for the deterministic case also holds for stochastic processes implies that methods designed to estimate the memory kernel, drift term, and fluctuating force term of this equation, as well as methods designed to propagate it numerically, can be applied to data obtained in molecular dynamics simulations that employ a stochastic thermostat or barostat.
Highlights
The concept of projection operators as a tool to reduce the dimension of physical systems goes back to the 1960s
Meyer et al.14,15 and te Vrugt et al.16,17 used timedependent projection operators similar to those of Mori to derive a general equation of motion for coarse-grained variables in nonequilibrium systems, including even systems under time-dependent external driving. (A similar attempt was made by Kawai and Komatsuzaki via the Zwanzig projection operator, but it turned out to be more involved mathematically than the Mori approach.18) Meyer et al introduced a general and fast method to compute the memory kernels appearing in their non-stationary Generalized Langevin Equation from a set of time-resolved values of an observable for individual trajectories
As such data are often accessible through molecular dynamics simulations, the question arises naturally if one can apply the same formalism in the context of stochastic microscopic propagators
Summary
The concept of projection operators as a tool to reduce the dimension of physical systems goes back to the 1960s. (Notably, a derivation of a non-stationary equation of motion using a time-dependent generalization of Mori’s projection operator formalism was presented by Nordholm in his Ph.D. thesis as early as 1972,9 but this was not taken up by the community as it was not published elsewhere.). Meyer et al. and te Vrugt et al. used timedependent projection operators similar to those of Mori to derive a general equation of motion for coarse-grained variables in nonequilibrium systems, including even systems under time-dependent external driving. Scitation.org/journal/jcp referring to the version of Meyer et al.) from a set of time-resolved values of an observable for individual trajectories.19 As such data are often accessible through molecular dynamics simulations, the question arises naturally if one can apply the same formalism in the context of stochastic microscopic propagators (e.g., dynamics generated using thermostats and barostats).
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