Abstract
We describe a method for computing transport coefficients from the direct evaluation of large deviation functions. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which are scaled cumulant generating functions analogous to the free energies. A diffusion Monte Carlo algorithm is used to evaluate the large deviation functions, from which arbitrary transport coefficients are derivable. We find significant statistical improvement over traditional Green–Kubo based calculations. The systematic and statistical errors of this method are analyzed in the context of specific transport coefficient calculations, including the shear viscosity, interfacial friction coefficient, and thermal conductivity.
Highlights
The evaluation of transport coefficients from molecular dynamics simulations is a standard practice throughout physics and chemistry
Such path ensemble free energies are known as large deviation functions [19], and with trajectory based importance sampling methods to aid in their calculation, we arrive at a method to evaluate transport coefficients that is both general and quickly convergent
We have explored the possibility of calculating transport coefficients from a large deviation function or a path ensemble free energy
Summary
The evaluation of transport coefficients from molecular dynamics simulations is a standard practice throughout physics and chemistry. Alternative methods exist that directly drive a current through the system by the application of specific boundary conditions [9,10] or by altering the equations of motion [11,12,13,14] These direct methods typically mitigate sampling difficulties by requiring that only the current is averaged rather than its time correlation function. The response is codified in the relative probability of a given current fluctuation, so this calculation is identical to the evaluation of a free energy, albeit in a path ensemble [18] Such path ensemble free energies are known as large deviation functions [19], and with trajectory based importance sampling methods to aid in their calculation, we arrive at a method to evaluate transport coefficients that is both general and quickly convergent
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