We derive an approach for extrapolating the free energy landscape of multicomponent systems in the grand canonical ensemble, obtained from flat- histogram Monte Carlo simulations, from one set of temperature and chemical potentials to another. This is accomplished by expanding the landscape in a Taylor series at each value of the order parameter which defines its macrostate phase space. The coefficients in each Taylor polynomial are known exactly from fluctuation formulas, which may be computed by measuring the appropriate moments of extensive variables that fluctuate in this ensemble. Here we derive the expressions necessary to define these coefficients up to arbitrary order. In principle, this enables a single simulation to provide complete thermodynamic information over a broad range of temperatures and chemical potentials. Using this, we also show how to combine a small number of simulations, each performed at different conditions, in a thermodynamically consistent fashion to compute properties at arbitrary temperatures and chemical potentials. We explicitly illustrate this for a binary fluid mixture which forms a negative azeotrope. This method significantly increases the computational efficiency of flat-histogram grand canonical Monte Carlo simulations.
Citation: The Journal of Chemical Physics
Pub Type: Journals
Monte Carlo, Grand canonical, Free energy, Fluid phase behavior, Thermodynamics