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| The '''isothermal-isobaric ensemble''' has the following variables:
| | Isothermal-Isobaric ensemble: |
| | Variables: |
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| * <math>N</math> is the number of particles | | * N (Number of particles) |
| * <math>p</math> is the [[pressure]] | | * p (Pressure) |
| * <math>T</math> is the [[temperature]] | | * T (Temperature) |
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| The classical [[partition function]], for a one-component atomic system in 3-dimensional space, is given by
| | Classical Partition Function (Atomic system, one-component, 3-dimensional space): |
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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]
| | <math> Q_{NpT} = \frac{1}{\Lambda^3} \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] |
| </math> | | </math> |
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| where
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| * <math> \left. V \right. </math> is the Volume: | | * <math> \beta = \frac{1}{k_B T} </math> |
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| *<math> \beta := \frac{1}{k_B T} </math>, where <math>k_B</math> is the [[Boltzmann constant]] | | * to be continued ... |
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| *<math> \left. \Lambda \right. </math> is the [[de Broglie thermal wavelength]]
| | == References == |
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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>
| | # D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Alogrithms to Applications", Academis Press |
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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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