Properties Derived from the Autocorrelation Function

This section outlines the statistical and physical quantities that can be computed as the integral of an autocorrelation function. For each property, a code skeleton is provided as a starting point for your calculations. All skeletons assume that you can load the relevant input data into NumPy arrays.

First, we discuss a few properties that may be relevant to multiple scientific disciplines:

• The uncertainty of the mean of time-correlated data

• The exponential and integrated autocorrelation time

The following physicochemical transport properties can be computed as autocorrelation integrals of outputs from molecular dynamics simulations, using the so-called Green-Kubo relations [Gre52, Gre54, Hel60, Kub57]. These properties have recently been referred to as diagonal transport coefficients [PDGB25].

• Shear viscosity, \(\eta\)

• Bulk viscosity, \(\eta_b\)

• Thermal conductivity, \(\kappa\)

• Electrical conductivity, \(\sigma\)

• Diffusion coefficient, \(D\)