Nonsteady stochastic properties of Markovian kinetics and macroscopic fluctuations

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Abstract
A stochastic evolution following a nonlinear Langevin equation with one degree of freedom was examined by a machine computation. The autocorrelation function of macroscopic fluctuations fixed by the time average instead of by the ensemble average is observed to have a long-time tail exhibiting a divergence of their power spectrum in the low-frequency limit. Such a divergence prevents the establishment of strongly steady stochastic process of fluctuations. The present results confirm that nonlinear Markovian kinetics keeps everlasting macroscopic fluctuations.