Non-equilibrium Molecular Dynamics
نویسندگان
چکیده
Statistical mechanics provides a well-established link between microscopic equilibrium states and thermodynamics. If one considers systems out of equilibrium, the link between microscopic dynamical properties and nonequilibrium macroscopic states is more difficult to establish [1,2]. For systems lying near equilibrium, linear response theory provides a route to derive linear macroscopic laws and the microscopic expressions for the transport properties that enter the constitutive relations in these laws. If the system is displaced far from equilibrium, no fully general theory exists to treat such systems. By restricting consideration to a class of non-equilibrium states which arise from perturbations (linear or non-linear) of an equilibrium state, methods can be developed to treat non-equilibrium states. Furthermore, non-equilibrium mole-cular dynamics (NEMD) simulation methods can be devised to provide estimates for the transport properties of these systems. Molecular dynamics is typically based on equations of motion derived from a Hamiltonian. However, often in the simulation of large complex systems, constraints are introduced to remove certain “fast” degrees of freedom from the system that are deemed to be unimportant for the phenomena under investigation. An important and prevalent example is the introduction of bond constraints to remove rapid vibrational degrees of freedom from the molecules of the system. Such constraints can be handled by the introduction of generalized coordinates and in these coordinates a Hamiltonian description of the equations of motion may be written. However, it is often more convenient to work with Cartesian coordinates with the holonomic constraints explicitly introduced in the equations of motion through Lagrange multipliers. One can treat the set of Lagrange multipliers as parameters that can be determined by
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