Gradient Monte Carlo: A High Throughput Method for Computing Thermodynamic Properties

There are many physical situations involving external fields or a non-isothermal environment. Monte Carlo (MC) simulations can be useful to understand such experimental systems at steady state. In this context, we formulate a general framework to study these systems via inhomogeneous MC simulations incorporating spatially varying temperature and gravitational fields. Using this approach, we study hard spheres in an external field with either uniform or non-uniform temperature. We present comprehensive results from our MC simulations, and compare these with theoretical results based on the Carnahan-Starling equation of state.

We consider next the case of mixtures of hard spheres and propose a new method for calculating the chemical potential of each species. The partial molar volumes are also computed and both chemical potential and partial molar volumes are compared to the predictions of the Boublik-Carnahan-Starling-Mansoori-Leland equation of state.

The Gradient Monte Carlo method proposed enables us to access a wide range of pressure-density values (states) in a single simulation and is a useful approach for high throughput computations of thermodynamic properties.