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| The '''isothermal-isobaric ensemble''' has the following variables:
| | In the Isothermal-Isobaric ensemble ... |
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| * <math>N</math> is the number of particles
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| * <math>p</math> is the [[pressure]]
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| * <math>T</math> is the [[temperature]]
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| The classical [[partition function]], for a one-component atomic system in 3-dimensional space, is given by
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| :<math> Q_{NpT} = \frac{\beta p}{\Lambda^{3N} N!} \int_{0}^{\infty} d V V^{N} \exp \left[ - \beta p V \right] \int d ( R^*)^{3N} \exp \left[ - \beta U \left(V,(R^*)^{3N} \right) \right]
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| </math>
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| where
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| * <math> \left. V \right. </math> is the Volume:
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| *<math> \beta := \frac{1}{k_B T} </math>, where <math>k_B</math> is the [[Boltzmann constant]]
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| *<math> \left. \Lambda \right. </math> is the [[de Broglie thermal wavelength]]
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| *<math> \left( R^* \right)^{3N} </math> represent the reduced position coordinates of the particles; i.e. <math> \int d ( R^*)^{3N} = 1 </math>
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| *<math> \left. U \right. </math> is the potential energy, which is a function of the coordinates (or of the volume and the reduced coordinates)
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| == Related reading ==
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| *[http://molsim.chem.uva.nl/frenkel_smit Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications", Second Edition (2002)] ISBN 0-12-267351-4
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| [[category: statistical mechanics]]
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