In an expanded ensemble simulation 68, both the
coordinates and the thermodynamic ensemble are treated as configuration
variables that can be sampled over. The probability of any given state
can be written as:
where is the
corresponding to the th thermodynamic state, and
is a user-specified weight factor corresponding to the th
state. This space is therefore a mixed, generalized, or expanded
ensemble which samples from multiple thermodynamic ensembles
simultaneously. is chosen to give a specific weighting of
each subensemble in the expanded ensemble, and can either be fixed, or
determined by an iterative procedure. The set of is
frequently chosen to give each thermodynamic ensemble equal probability,
in which case is equal to the free energy in non-dimensional
units, but they can be set to arbitrary values as desired. Several
different algorithms can be used to equilibrate these weights, described
in the mdp option listings.
In GROMACS, this space is sampled by alternating sampling in the
and directions. Sampling in the
direction is done by standard molecular dynamics
sampling; sampling between the different thermodynamics states is done
by Monte Carlo, with several different Monte Carlo moves supported. The
states can be defined by different temperatures, or choices of
the free energy variable, or both. Expanded ensemble
simulations thus represent a serialization of the replica exchange
formalism, allowing a single simulation to explore many thermodynamic
states.