softmatter:Thermodynamic Ensembles

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The thermodynamical ensemble sampled in a molecular simulation is determined by the set of constraints placed on the system. The most commonly simulated statistical ensembles are:

  • The Microcanonical (NVE) Ensemble -- An ensemble of systems with the same total energy.
  • The Canonical (NVT) Ensemble -- An ensemble of systems with the same number of particles, volume, and temperature. The temperature is fixed by coupling to a heat reservoir.
  • The Grand Canonical Ensemble -- An ensemble of systems with constant chemical potential, volume, and temperature. The systems can exchange energy with a heat reservoir and exchange particles with a particle reservoir.

The ensembles are characterized by their state functions, which describe the statistical weight of a given microstate in the ensemble :

Microcanonical: \; \Omega(U,V,N) = e^{\beta TS}

Canonical: \; Z(T,V,N) = e^{- \beta A}

Grand canonical: \; \Xi(T,V,\mu) = e^{\beta P V}

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