Motion and Macroscopic Observables

Perhaps one of the greatest successes of the molecular dynamics (MD) method is its ability both to predict macroscopically observable properties of systems, such as thermodynamic quantities, structural properties, and time correlation functions, and to allow modeling of the microscopic motions of individual atoms. From modeling, one can infer detailed mechanisms of structural transformations, diffusion processes, and even chemical reactions (using, for example, the method of ab initio molecular dynamics).Such information is extremely difficult, if not impossible, to obtain experimentally, especially when detailed behavior of a local defect is sought. The variety of different experimental conditions that can be mimicked in an MD simulation, such as 

Consider a classical N-particle system in d dimensions in isolation from any external influences. The system is considered to have Nf total degrees of freedom, which, in general, can differ from dN. If, for example, there are constraints on the system, then N = dN -. The physical state of such a 

Hamilton s equations can be cast in the form of an equation for F by introducing the Poisson bracket /, g between two functions on the phase space /(F) andg(F)i  

it is straightforward to show that the phase space vector evolves according to 

Equation [8] can be solved, in principle, to yield the time evolution 

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