Flattening the Energy Distribution Multicanonical Sampling and Related Methods

1 Flattening the Energy Distribution Multicanonical Sampling and Related Methods 

Here an additional distinction is to be made between thermodynamic averages of a conformational observable such as the internal energy, which converges well if potential minima are correctly sampled, and statistical properties such as free energies, which depend on the entire partition function. 

Consider, for instance, the free energy A( ) projected onto important degrees of freedom. This is a potential of mean force along and is obtained by integrating out all the other degrees of freedom, q. It is related to the probability of finding the system at a particular value of by 

Since the potential of mean force is a statistical property, it is insufficient to calculate it directly by importance sampling which, by design, emphasizes potential minima 

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