Applications to Microcanonical Simulations

Monte Carlo methods can also be applied to systems in the microcanonical ensemble,and the techniques just described can be extended to this ensemble as well. For a cluster of N atoms with the same mass m, microcanonical averages of observables are obtained by calculating statistical expectations using the density function 

Either parallel tempering or J-walking in the microcanonical ensemble consists of taking configurations from a walk at high energy Ef, rather than 

Microcanonical parallel tempering has been extended to the molecular dynamics ensemble by introducing the appropriate center of mass and angular momentum constraints, the details of which can be found elsewhere.  

Another class of methods that has been used to remove sampling difficulties is based on what is often called the multicanonical ensemble These methods have also been called entropy sampling methods,for reasons that are made clear below. It is easiest to understand the multicanonical methods by considering the full classical canonical coordinate-momentum distribution 

As is discussed in many elementary treatments of statistical mechanics, 0(E) is a rapidly increasing function of the energy. Owing to the decay of the exponential factor in Eq. [42], p(p,E) is a sharp Gaussian distribution, and is peaked about the mean energy associated with the inverse temperature p. 

---