Research Interests

Since my formal retirement my main area of interest has moved towards the foundations of statistical mechanics and thermodynamics. In particular I am interested in exploring the nature of irreversibility and equilibrium. In a number of papers on statistical mechanics I have argued that, in order to reconcile the Boltzmann and Gibbs approaches to statistical mechanics, it is necessary to abandon the binary property of being or not being in equilibrium in favour of a continuous property which I call 'commonness'. Related to this I contend that rather than a preoccupation with 'local' increase in entropy a more fruitful approach is to consider the global picture where thermodynamic-like behaviour is associated with entropy mostly fluctuating to values close to its maximum with infrequent larger fluctuations to lower values. In thermodynamics I have investigated the problem of equilibrium processes and the contentious question of negative temperatures. A well-known puzzle in thermodynamics and statistical mechanics is that critical phenomena, understood as either discontinuities of densities (first-order transitions) or singularities in response functions (second or higher order transitions) occur in theoretical models only in the thermodynamic limit. Reimer Kuehn, Roman Frigg and I have explored this problem. Using the renormalization group and finite-size scaling, we give a definition of a large but finite system and argue that phase transitions are represented correctly, as incipient singularities in such systems.

In the past series expansion methods have been used with one expansion parameter and numerical coefficients to obtain critical properties at one point in phase space. The object of my research with Byron Southern of the University of Manitoba is to provide the beginning of a general methodology for using series to explore the whole of the phase space. We are using the finite-lattice method to develop series where the coefficients are polynomial functions of the Boltzmann factors for a number of other couplings. We are currently investigating a modified three-state Potts model on a triangular lattice with a chiral term around each triangle. This chiral term is of particular interest as it forms the basis for the development of lattice models with directional bonding. These have been used to simulate water-like behaviour.