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10.5.3: Isothermal-isobaric and grand canonical ensembles

  • Page ID
    5258
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    Also useful are the isothermal-isobaric and grand canonical ensembles, which are defined just as they are for the classical cases:

    • isothermal-isobaric:

    \[\Delta(N,P,T) = \int_0^{\infty}dV e^{-\beta PV} Q(N,V,T) =\int_0^{\infty} dV {\rm Tr}(e^{-\beta (H+PV)}) \nonumber \]

    • grand canonical ensembles

    \[ {\cal Z}(\mu,V,T) = \sum_{N=0}^{\infty}e^{\beta \mu N}Q(N,V,T) = \sum_{N=0}^{\infty} {\rm Tr}(e^{-\beta (H-\mu N)}) \nonumber \]


    This page titled 10.5.3: Isothermal-isobaric and grand canonical ensembles is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Mark Tuckerman.