A simple nonparametric procedure is devised for constructing Boltzmann entropy functions from statistically weighted entropy differences calculated from overlapping histograms. The method is noniterative, avoids numerical problems associated with large state densities, and accommodates variable bin widths for reducing systematic and statistical errors inherent to histogram techniques. Results show that the procedure can yield thermodynamic functions for an Ising spin lattice model that have average errors comparable to ones obtained from a conventional approach. Analysis of thermofunctions computed for a polyalanine peptide simulated by hybrid Monte Carlo replica exchange indicates that method performance can be enhanced through the use of nonuniform state space discretization schemes. An extension of the reweighting procedure for multidimensional applications is presented through calculations of vapor-liquid equilibrium densities of a model fluid simulated by grand canonical replica exchange.

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For simulations in the grand canonical ensemble, the probability distribution of the number of particles N and the total potential energy U may be written as P(N,UB,V,T)=exp[βU+BNlnN!+S(N,U)kB]Ξ(B,V,T), where V is the system volume, Ξ(B,V,T) is the partition function, and B is a function of the chemical potential μ (Ref. 79). The particle pair potential describing the Lennard-Jones system is u(r)=4ε(σr)12(σr)6, where r is the interparticle separation distance, ε is the potential well-depth, and σ is the separation corresponding to zero potential. Results reported for U, V, T, and S are expressed in units of ε, σ3, εkB, and kB, respectively.

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It is noted that I and J in the sum mwIJ,m denote UI and UJ values of the same lnΩ(U) curve for constant N whereas I and J in Eq. (6) correspond to lnΩ(U) curves for NI and NJ.

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