Calculation of the Stability of Phase Space Trajectories Using Molecular Dynamics Simulations

Significant Achievements, Anticipated Outcomes and Future Work

A fluctuation theorem that describes the probability of observing violations of the Second Law of Thermodynamics was developed using the Lyapunov weight formula has now been published. This formula expresses the probability of trajectories in phase space being observed in terms of their escape from a phase space volume, which is related to the sum of the positive Lyapunov exponents of the system.

The validity of the conjugate pairing rule (CPR), describing the properties of pairs of Lyapunov exponents, was investigated in the weak field limit (weak shear flow or colour field) in an ergostatted system for various system sizes and by different calculation methods. The deviations with field from equilibrium values were analysed and compared with theory. These studies are being extended to thermostatted systems and systems at fixed phase space compression.

CPR was also investigated in systems in which a fraction of the total number of particles was ergostatted and shown to follow a simple pairing rule with increasing field strength. Deviations with fraction size were also investigated.

In order to obtain nonequilibrium steady states in simulations, it is necessary to use artificial thermostats. A class of thermostats (“mu” thermostats) are being studied in order to determine the properties of thermostats that make them physically acceptable. The results demonstrate that thermostats which violate Gauss’s principle act like a dissipative field, driving the system away from equilibrium. A series of “mu” thermostats fixing higher moments of the temperature were also explored. CPR was also investigated in these systems as was the equivalent nonequilibrium system in the weak field limit. These studies are currently being extended to larger systems and longer timescales.

Analogous systems in which a fraction of the particles were thermostatted were also investigated in a similar manner to above. Studies were initiated aimed at identifying the temporal and average contributions of various locations of the system and of given particles. CPR and phase space dimensionality loss have again been the focus of this work.

Computational Techniques Used

Equilibrium and nonequilibrium molecular dynamics simulation methods are being used and are developed in this project. Access to supercomputer facilities is required to obtain statistically valid data for small systems and to study large systems.

Publications, Awards and External Funding

External Funding and Awards

ARC Large Grant 2001-2003 Theoretical and computational studies of nonequilibrium fluids, Debra J. Bernhardt(Searles) (CI), Denis J. Evans (AI)
ARC Discovery Grant 2002-2004 Modelling of adsorption dynamics in microporous solids based on molecular dynamics computations, Suresh Bhatia (CI) and Debra J. Bernhardt(Searles) (CI)

Publications

O. Jepps, D. J. Evans, D. J. Searles, "The fluctuation theorem and Lyapunov weights", Physica D, 187, (2004), 326-337.
E. Mittag and D. J. Evans, "Time Dependent Fluctuation Theorem", Phys. Rev. E 67, (2003) 026113.
S. Hess, M. Kröger, D. J. Evans, "Crossover between short- and long-time behavior of stress fluctuations and viscoelasticity of liquids", Phys. Rev. E 67, (2003) 042201.