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Ben Leimkuhler

University of Edinburgh

Equilibrium Methods for Nonequilibrium Modelling

Abstract:

Molecular dynamics (MD), if properly used, is an extraordinary tool, but the portion of phase space accessible to standard MD is often inadequate due to the presence of energetic and/or entropic barriers. For this reason molecular dynamics is increasingly used as part of sophisticated schemes which force the system into rarely visited regions of phase space, placing increasing demands on the simulation methodology. In particular, thermal equilibration (relaxation of trajectories to equidistribution of energy) is often difficult, and modern techniques require us to compute many well- equilibrated trajectories, in regions of high dynamical activity, with minimal disturbance of dynamics. A thermostat is a perturbation of Hamiltonian dynamics which aids in the recovery of averages. I will discuss the motivation and aim of thermostatting and describe ongoing work on the development of flexible families of thermostatting methods for molecular dynamics. Hamiltonian based thermostatting methods allow for the use of symplectic integrators which in turn enable estimation of the error in averages as a function of the integration stepsize. Alternatively, stepsize-dependent reweighting formulas allow thermodynamic computations to performed with higher accuracy. While ergodicity-enhancing devices can be incorporated into the Hamiltonian framework, it appears that some type of stochastic perturbation is helpful for obtaining a rapid convergence to canonical sampling in many practical situations. I will describe alternative formulations for stochastic dynamics, generalizing Langevin dynamics but including kinetic energy control, each of which can be analyzed using standard methods. This talk discusses recent work with several collaborators: S. Bond (Illinois), E. Noorizadeh (Edinburgh), and F. Theil (Warwick).