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

The Lyapunov exponents of a liquid system are a measure of the dynamical stability of a system and can be related to transport properties of the liquid such as the viscosity and the thermal conductivity. If the spectrum of Lyapunov exponents is symmetric, calculation of these liquid state properties from the Lyapunov exponents is facilitated. Studies of the structure of the spectrum are therefore being carried out. A number of relationships between the Lyapunov exponents and properties of fluids have now been developed. In this project new relationships will be derived and checked using numerical simulation.

Numerical simulations of fluids flowing through micropores have been carried out for various systems: atomic fluids, rigid molecules and molecular fluids. In order to achieve this the configurational temperature is used to measure and/or constrain the temperature. The configurational temperature is a new expression for the thermodynamic temperature that is obtained by performing a functional differentiation of the entropy of a microcanonical system with respect to the thermodynamic internal energy. The new temperature is entirely dependant on configurations and thereby circumvents difficulties in defining streaming velocities in complicated geometries.

Principal Investigator

Denis Evans
Physical and Theoretical Chemistry


s02, r61

Facilities Used



Jerome Delhommelle
Owen Jepps
Janka Petravic
Physical and Theoretical Chemistry

Emil Mittag
Computational Quantum Chemistry

Debra Bernhardt
Department of Chemistry
Griffith University

RFCD Codes


Significant Achievements, Anticipated Outcomes and Future Work

A new derivation of the fluctuation theorem that describes the probability of observing violations of the Second Law of Thermodynamics has been developed using the Lyapunov weight formula. 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. Tests of this formula have been carried out and will be submitted for publication early in 2002.

The semi-empirical scaling law between transport coefficients and excess entropy has been systematically studied for 3 types of atomic potentials (soft, LJ and WCA) along an isochore and an isobar. The disagreement with the law is explained in terms of differences between 2-particle and total excess entropy, the relative contributions of interaction and thermal motion to transport at different state points and discrepancy between Enskog hard-sphere estimate of collision frequency and the Maxwell relaxation time.

In the second project simulations of confined fluids have been carried out for atomic and molecular fluids. The configurational temperature profile in these fluids has been obtained. This work has been published in high profile journals.


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 in investigations of the influence of system size.


Publications, Awards and External Funding

J. Delhommelle, D. J. Evans, Configurational temperature profile in confined fluids. I. Atomic fluid, J. Chem. Phys., 114, 2001, 6229-6235.

J. Delhommelle, D. J. Evans, Configurational temperature profile in confined fluids. II. Molecular fluids, J. Chem. Phys., 114, 2001, 6236-6241.

J. Delhommelle, D. J. Evans, Comparison of thermostatting mechanisms in NVT and NPT simulations of decane under shear, J. Chem. Phys., 115, 2001, 43-49.