Liquid-Vapor Equilibria using the Wang-Landau Algorithm

1 Liquid-Vapor Equilibria using the Wang-Landau Algorithm 

The acceptance criteria for particle insertion and deletion moves are determined from the detailed balance condition applied to these probabilities. The final expressions are 

Recognizing that / = /cx I Arln F - InAH from Chap. 1, all three acceptance criteria can be expressed as 

We can, therefore, let /cx be the subject of our calculations (which we approximate via an array in the computer). Post-simulation, we desire to examine the joint probability distribution p(N, U) at normal thermodynamic conditions. The reweighting ensemble which is appropriate to fluctuations in N and U is the grand-canonical ensemble consequently, we must specify a chemical potential and temperature to determine p. Assuming -7CX has converged upon the true function In f2ex, the state probabilities are given by 

The density dependence of the entropy can also be studied by introducing fluctuations in volume rather than particle number. Typically the particle number approach is favored the computational demands of volume scaling moves scale faster with system size than do addition and deletion moves. Nevertheless, the Wang-Landau approach provides a means for studying volume fluctuations as well. In this case, the excess entropy is determined as a function of volume and potential energy for fixed particle number one, therefore, calculates (V, U). Here the microstate probabilities follow  

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