One way to make your dynamics explore more of phase space is to force it out of regions it has already explored. Metadynamics does this dynamically by intermittently adding bias potentials (typically Gaussians) to the system Hamiltonian. These bias potentials are functions of user defined collective variables, which should be chosen such that states of interest can be clearly distinguished from each other. The figure below gives a good example of how metadynamics proceeds; a common analogy is that you are exploring a potential energy surface that is slowly with sand/water around the current state. In the long time limit, the bias potentials should sum up to the free energy, but with the opposite sign.
The main difficultly of this method is determining what collective variables need to be considered in order to fully describe your system. Its an area of active of research to develop fairly general collective variables (or at least guidelines for their selection) for a variety of systems. As an example of what these collective variables can look like, consider , a paper by Michele Parrinello, who originally proposed the concept of metadynamics. In this paper, they define an enthalpic and an entropic collective variables in order model crystal formation of aluminum and sodium.
- Pablo M. Piaggi, Omar Valsson, and Michele Parrinello PRL 119, 015701 (2017)