Predicting the free energy landscape of multicomponent fluids

We derive a statistical mechanical framework for predicting the grand canonical free energy landscape of multicomponent fluids at low temperatures from flat-histogram Monte Carlo simulations performed at higher ones. This is... [ view full abstract ]

We derive a statistical mechanical framework for predicting the grand canonical free energy landscape of multicomponent fluids at low temperatures from flat-histogram Monte Carlo simulations performed at higher ones. This is accomplished by expanding the landscape in a Taylor series at each point on the surface defined by the sampling order parameter; we illustrate how all equations necessary to precisely obtain the coefficients in these series may be obtained using classical statistical mechanics, and may be computed using data trivially available during the simulation. This approach allows us to extrapolate the thermodynamic behavior of systems which undergo both first order and continuous phase transitions upon cooling using only a single simulation performed only at a higher temperature.  After surveying a variety of different fluid systems, we identify a range of temperature differences over which the extrapolation of high temperature simulations tends to quantitatively predict various thermodynamic properties at lower ones. Beyond this range, extrapolation still provides a reasonable estimate of the free energy landscape; this prediction then requires less computational effort to refine via additional simulation(s) at the desired temperature than construction of the surface without any initially informed estimate. In either case, this method significantly increases the computational efficiency of flat-histogram Monte Carlo simulations when investigating thermodynamic properties of fluids over a wide range of temperatures.