Green–Kubo formula derived from large deviation statistics

Numerical calculations for many physical systems including chaos and turbulence have been greatly developed in recent years. We often investigate the characteristics of the time series for chaotic systems and study the essential laws underlying its time series. We show the important characteristics which are sometimes not pointed out. One of them is the Green–Kubo formula, which holds for the time series that satisfies the large deviation statistics. Extended version for the relation is shown in this paper and a simple example is given. The relationship between the Green–Kubo formula and the large deviation statistics is emphasized.