Nonequilibrium Molecular Dynamics and Linear Response

Transport coefficients of molecular model systems can be calculated by two methods [8] Equilibrium Green-Kubo (GK) methods where one evaluates the GK-relation for the transport coefficient in question by performing an equilibrium molecular dynamics (EMD) simulation and Nonequilibrium molecular dynamics (NEMD) methods. In the latter case one couples the system to a fictitious mechanical field. The algebraical expression for the field is chosen in such a way that the currents driven by the field are the same as the currents driven by real Navier-Stokes forces such as temperature gradients, chemical potential gradients or velocity gradients. By applying linear response theory one can prove that the zero field limit of the ratio of the current and the field is equal to the transport coefficient in question. 

Several transport properties can be evaluated from equilibrium simulations with use of linear response theory, which relates correlation fimctions of spontaneously fluctuating molecular properties to phenomenological transport coefficients. These relations can be used to evaluate diffusion coefficients, thermal conductivities, viscosities, IR spectra, and so on. However, most of these properties are evaluated more directly using appropriately devised techniques of nonequilibrium molecular dynamics. Particularly challenging for polymers is the direct... 

Beyond linear response theory, molecular dynamics has the capability in principle of simulating processes which are well away from equilibrium. This capability has been exploited in the development of nonequilibrium molecular dynamics, as described by Hoover and Ashurst, and recently reviewed by Hoover.The technique is to modify the equations of motion, which in effect couples the system to momentum and energy reservoirs, so that the computer can simulate a nonequilibrium steady state. Applications Include viscous flows, heat flows, and chemical reactions. 

An alternative to using equilibrium MD for computing transport coefficients is to use nonequilibrium molecular dynamics (NEMD) in which a modified Elamiltonian is used to drive the system away from equilibrium. By monitoring the response of the system in the limit of a small perturbation, the transport coefficient associated with the perturbation can be calculated. There is a rich literature on the use of NEMD to calculate transport coefficients the interested reader is referred to the excellent monograph by Evans and Morriss and the review article by Cummings and Evans.The basic idea behind the technique is that a system will respond in a linear fashion to a small perturbation. The following linear response theory equation is applicable in this limit ... 

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