The constant-pressure, constant-temperature (NPT) molecular dynamics approach is re-examined from the viewpoint of deriving a new measure-preserving reversible geometric integrator for the equations of motion. The underlying concepts of non-Hamiltonian phase-space analysis, measure-preserving integrators and the symplectic property for Hamiltonian systems are briefly reviewed. In addition, current measure-preserving schemes for the constant-volume, constant-temperature ensemble are also reviewed. A new geometric integrator for the NPT method is presented, is shown to preserve the correct phase-space volume element and is demonstrated to perform well in realistic examples. Finally, a multiple time-step version of the integrator is presented for treating systems with motion on several time scales.
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