Stochastic Dynamics in Irreversible Nonequilibrium Environments. 3. Temperature-Ramped Chemical Kinetics

Abstract

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.

Derivation of the generalized Langevin equation in nonstationary environments

“…For the last decade there have been several attempts at establishing the nonstationary representation termed as the irreversible generalized Langevin equation (iGLE). [25][26][27][28][29][30][31][32][33][34] In particular, the idea of generalized friction kernel 28, 34 dependent on both the time values at the past and the present was proposed. As the (nonstationary) bath relaxes to the equilibrium state as time proceeds, the friction kernel is shown to converge to the usual equilibrium one, which depends only on the time difference.…”

“…As the (nonstationary) bath relaxes to the equilibrium state as time proceeds, the friction kernel is shown to converge to the usual equilibrium one, which depends only on the time difference. The generalization of the fluctuation-dissipation theorem was also proposed: the autocorrelation of the random force averaged over a given distribution of the initial condition of the bath dof corresponds to the generalized time-dependent friction kernel [28][29][30][31][32][33][34] or with an exponentially dumping correction term, [25][26][27] depending on how to formulate the iGLE. The iGLE can be applied not only to phenomena subject to an outside force that changes the solvent response, 28 but also to systems whose nonstationarity is induced by the dynamics of the system itself.…”

“…30 The growth of polymer was taken as an example where the property of the environment changes with the increase of the polymer length. It can also be applied to temperature-ramped chemical reactions 31 where the environment temperature changes with time due to heating, for example, by a laser pulse. A further extension of iGLE (Ref.…”

An idealized model for nonequilibrium dynamics in molecular systems

“…1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 In recent work, 16,17,18,19,20 it was suggested that in many instances, the environment is not stationary, and as such a nonstationary version of the GLE would be desirable. In principle, it is easy to write a nonstationary GLE aṡ…”

“…(1) and as such is an example of nonstationary stochastic dynamics. In recent work, 16,17,18,19,20 a generalization of this model was developed which includes arbitrary nonstationary changes in the strength of the friction, but like the xGLE model does not include changes in the response time. As such it is not quite the ultimately desired nonstationary GLE.…”