"Thermodynamics" from Time Series Data Analysis

We propose a derivation of statistical laws from time series data analysis on the analogy of the thermodynamics. Recently, Sekimoto and Sasa reconstructed thermodynamics of systems, which are governed by the Langevin equations. We construct \thermodynamics" by applying their approach to the Auto Regressive type models, in which the random uctuation is no more thermal one. Since the detailed balance is broken in such system, irreversible circulation of uctuation appears. We apply our arguments to the zero-power point reactor kinetics model. We try to derive new \thermodynamical" laws from actually data observed in a test nuclear reactor.