ensemble - where particle number, volume
and energy are the external thermodynamic control variables -
by suitable Laplace transforms of its
partition function.
Thermodynamically this corresponds to Legendre transforms
of the associated thermodynamic potentials where
intensive and extensive conjugate variables are interchanged.
In thermodynamics, this task is achieved by
a ``sufficiently weak'' coupling of the original system
to an appropriate infinitely large bath or reservoir
via a link that establishes thermodynamic equilibrium.
The same basic idea is instrumental in generating distribution
functions of such ensembles by computer simulation.
Additional degrees of freedom that control the quantity under consideration
are added to the system. The simulation is then performed in the
extended microcanonical ensemble with a modified total energy as a constant of
motion. This system has the property that after the correct integration
over the additional degrees of freedom has been performed the
distribution function of the targeted ensemble is recovered.
Two important special cases are: thermostats and barostats, which are used to
impose temperature instead of energy and / or pressure instead of volume
as external control parameters [12,13,17,26,27,28,29,30,31].