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note
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Several technical aspects in obtaining the TCFs should be mentioned. First, the interval of the initial times should not be too small compared to the decay time of the TCP, so that the averaged events in Eq. (11) are statistically independent as required in an ensemble average. Since the statistical uncertainty is of order 1/√n, a TCP with short-time correlation can be determined with greater statistical precision because the number of terms in the average, n, is larger. On the other hand, in order to achieve a desired accuracy for a TCP with a slow decay rate, long MD runs with a large number of time steps are needed in order to ensure enough number of independent events in the averaging. More accurate results can usually be obtained for the single-particle TCFs, which are one-particle quantities, such as the velocity autocorrelation function. Since each single-particle trajectory can be independently exploited in the averaging process, so that the total number of events in the average is increased N times for a system with N particles. However, most of the practical TCFs, such as that corresponding to the momentum and thermal transport coefficients, are collective TCFs involving many particles.
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