Nonequilibrium molecular dynamics NEMD

Evans and Baranyai [51, 52] have explored what they describe as a nonlinear generalization of Prigogine s principle of minimum entropy production. In their theory the rate of (first) entropy production is equated to the rate of phase space compression. Since phase space is incompressible under Hamilton s equations of motion, which all real systems obey, the compression of phase space that occurs in nonequilibrium molecular dynamics (NEMD) simulations is purely an artifact of the non-Hamiltonian equations of motion that arise in implementing the Evans-Hoover thermostat [53, 54]. (See Section VIIIC for a critical discussion of the NEMD method.) While the NEMD method is a valid simulation approach in the linear regime, the phase space compression induced by the thermostat awaits physical interpretation even if it does turn out to be related to the rate of first entropy production, then the hurdle posed by Question (3) remains to be surmounted. 

Perhaps the most common computer simulation method for nonequilibrium systems is the nonequilibrium molecular dynamics (NEMD) method [53, 88]. This typically consists of Hamilton s equations of motion augmented with an artificial force designed to mimic particular nonequilibrium fluxes, and a constraint force or thermostat designed to keep the kinetic energy or temperature constant. Here is given a brief derivation and critique of the main elements of that method. 

Nonequilibrium molecular dynamics (NEMD) Monte Carlo heat flow simulation, 71-74 theoretical background, 6 Nonequilibrium probability, time-dependent mechanical work, 51-53 Nonequilibrium quantum statistical mechanics, 57-58... 

It should be mentionned that the result of q-dependent chain orientation in shear was also found by nonequilibrium molecular dynamics (NEMD) simulations by Kroger et al [32], The increasing power of computational techniques will surely result in increased accuracy and usefulness of this type of numerical simulation. 

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. 

One easy extension of equilibrium molecular dynamics is the computation of the properties of condensed matter systems in the presence of external fields. Many experiments are done by applying an external field, whether it be an electric field, heat gradient, or some type of flow. Usually, the experimentalist waits some time for the system under investigation to reach a steady state in the presence of the applied field. Measurements are then performed to deduce structural or dynamical information. Performing this task on a computer is what is commonly known as nonequilibrium molecular dynamics (NEMD). It is nonequilibrium in the sense that, in the presence of an external field, the system at the steady state will be in a state of lower entropy. Upon removing the external field, the system will return to the state of maximum entropy or the equilibrium state. 

Thus, we have a set of equations of motion given by Eqs. [91] that describe a general coupling to an external field. Our objective is to compute averages of functions of the phase space when the system coupled to the external field has reached a steady state. This is the procedure of nonequilibrium molecular dynamics (NEMD) simulations. An illustrative example to consider is the computation of the shear viscosity from Newton s law of viscosity, which reads ... 

For nonequilibrium molecular dynamics (NEMD), the short-range van der Waals interactions between all particles, both solvent and ions, are modeled with a truncated and shifted Letmard-Jones (L-J) potential. 

In the method of nonequilibrium molecular dynamics (NEMD), transport processes are usually driven by boundary conditions. For example, the calculation of shear viscosity is based on the Lees-Edwards flow-adapted sliding brick periodic boundary conditions (PBCs) (Panel 4 or their equivalent Lagrangian-rhomboid... 

The favorable thermal properties of nanofluids and the possibility of their application in a large number of areas have lead to exploration of different methods to predict properties of nanofluids and mechanisms that enhance their thermal performance. Classical MD is an attractive option for such studies. Within MD, transport coefficients can be calculated using either equilibrium molecular dynamics (EMD) or nonequilibrium molecular dynamics (NEMD). 

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 ... 

Dynamic processes in atomic liquids are nowadays well understood in terms of kinetic theory and computer calculations. Transport coefficients and dynamic scattering functions of liquid argon, for example, are well reflected by kinetic theories and equilibrium (MD) as well as nonequilibrium molecular dynamics (NEMD) calculations using Lennard-Jones (U) pair potentials. 

The apphcation of MD to study systems that are undergoing transformation towards a new equilibrium state belongs to the family of methods called nonequilibrium molecular dynamics (NEMD). In implementation, NEMD simulations usually take one of two forms either a driving force is introduced that maintains the system out of equilibrium at steady state, or else a perturbation is introduced and the system is studied as it relaxes toward equilibrium. The latter is not at steady state, and thus the system is constantly evolving, although not necessarily smoothly in time and/or space. Such unsteady-state NEMD simulations can in some circumstances encounter limitations in their ability to sample adequately some of the dynamics. Nevertheless, most of the MD studies of crystallization for polymers to date are of the unsteady NEMD type. 

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