A fractional Brownian motion model for time series produced by constant temperature molecular dynamics simulations

In the present work we performed an analysis of time series of instantaneous temperature and pressure produced during constant temperature molecular dynamics. Simulations were applied to a nickel oxide grain boundary for a temperature range 0.15-0.80T(m), T-m being the melting point of the system. We performed a series of analysis for these time series including test for randomness, power spectrum, Hurst exponent and structure function test. Evidence of fractional Brownian motion was found. Pressure presents 1/f over the whole range of frequencies of the system while temperature presents a two-regime behavior: white noise at low frequencies and 1/f(alpha) at high frequencies with alpha increasing as a function of temperature. The origins of this behavior are discussed.