Alladi Ramakrishnan Hall

Non-Boltzmann Monte Carlo Methods

K. P. N. Murthy

Univ of Hyderabad

Boltzmann sampling based on Metropolis algorithm has been extensively used for simulating a
canonical ensemble. An estimate of a mechanical property, like energy, of an equilibrium system,
can be made by averaging over a large number micro states generated by Boltzmann Monte Carlo
methods. However a thermal property like entropy is not easily accessible to these methods. The
reason is simple. We can assign a numerical value for energy to each micro state.
But we can not carry out such an assignment for entropy. Entropy is not a property of a microstate. It belongs to all the micro states. It is a collective property.

Toward calculating entropy and other thermal properties, a non-Boltzmann Monte Carlo method called Umbrella sampling was proposed in the mid-seventies of the last century. Umbrella sampling has since undergone several metamorphoses and we have now multi-canonical Monte Carlo, entropic sampling, flat histogram methods, Wang-Landau algorithm etc. This class of methods generates non-Boltzmann ensembles which are un-physical. However, physical quantities can be calculated by un-weighting and re-weighting techniques. In this talk I shall tell you of a few non-Boltzmann Monte Carlo methods with emphasis on recent developments.