Monday 10 November - Friday 14 November 2003
The Australian Mathematical Sciences Institute, Melbourne, Australia

John Valleau – University of Toronto

Thermodynamic-Scaling Monte Carlo and the Statistical Thermodynamics of Small Systems

Two-dimensional thermodynamic-scaling allows detailed study of a substantial region of thermodynamic state space in a single Monte Carlo (MC) realisation; for example one can obtain essentially continuous data (on free energies as well as ensemble averages) over large regions of temperature and density (TDSMC) or of temperature and chemical potential (TMuSMC).

A general problem of interpreting MC data is that for the small systems that are actually accessible the derived behaviour differs from that of a bulk system (i.e. from the so-called “thermodynamic limit”); in particular the size-dependent behaviour depends on the statistical ensemble employed (canonical, isothermal-isobaric, grand canonical, Gibbs), and alternative choices of thermodynamic definitions (even though these may be equivalent in the bulk limit) can lead to apparently discrepant behaviours. It turns out that thermodynamic-scaling results prove effective in examining such problems (including even ensemble dependences). We explain how this is possible, and review some of the small-system consequences (using TDSMC results for Lennard-Jonesium as an example). The results tend to point out circumstances where small-system Monte Carlo “thermodynamic” data must be interpreted in an especially critical way.