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Extended System Approach

In the framework of statistical mechanics all ensembles can be formally obtained from the microcanonical $ NVE$ ensemble - where particle number, volume and energy are the external thermodynamic control variables - by suitable Laplace transforms of its partition function. Thermodynamically this corresponds to Legendre transforms of the associated thermodynamic potentials where intensive and extensive conjugate variables are interchanged. In thermodynamics, this task is achieved by a ``sufficiently weak'' coupling of the original system to an appropriate infinitely large bath or reservoir via a link that establishes thermodynamic equilibrium. The same basic idea is instrumental in generating distribution functions of such ensembles by computer simulation. Additional degrees of freedom that control the quantity under consideration are added to the system. The simulation is then performed in the extended microcanonical ensemble with a modified total energy as a constant of motion. This system has the property that after the correct integration over the additional degrees of freedom has been performed the distribution function of the targeted ensemble is recovered. Two important special cases are: thermostats and barostats, which are used to impose temperature instead of energy and / or pressure instead of volume as external control parameters [12,13,17,26,27,28,29,30,31].



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Next: Barostats Up: Molecular Dynamics and ab Previous: Numerical Integration   Contents   Index
Costas Bekas 2008-09-04