Single trajectory transport coefficients and the energy landscape by molecular dynamics simulations

The Green-Kubo (GK) method is widely used to calculate the transport coefficients of model liquids by Molecular Dynamics (MD) simulation. A reformulation of GK was proposed by Heyes et al. [J. Chem. Phys. 150, 174504 (2019)], which expressed the shear viscosity in terms of a probability distribution function (PDF) of "single trajectory (ST) viscosities," called "viscuits." This approach is extended here to the bulk viscosity, thermal conductivity, and diffusion coefficient. The PDFs of the four STs expressed in terms of their standard deviations (calculated separately for the positive and negative sides) are shown by MD to be statistically the same for the Lennard-Jones fluid. This PDF can be represented well by a sum of exponentials and is independent of system size and state point in the equilibrium fluid regime. The PDF is not well reproduced by a stochastic model. The PDF is statistically the same as that derived from the potential energy, u, and other thermodynamic quantities, indicating that the transport coefficients are determined quantitatively by and follow closely the time evolution of the underlying energy landscape. The PDFs of out-of-equilibrium supercooled high density states are quite different from those of the equilibrium states.