The Characteristic Noise Induced by the Continious Measurements in Classical Open Systems

We proposed the modified version of quantum-mechanical theory of continuous measurements for the case of classical open systems. In our approach the influence of measurement on evolution of distribution function of an open system is described by the Fokker-Planck equation of a special form. The diffusion tensor of this equation is uniquely defined by a type of the measured quantity. On the basis of the approach proposed the stationary states of the linear dissipative systems, induced by measurements in them, are considered. Also we demonstrate on the simple example, how in the conservative system, consisting of noninteracting parts, measurement of the integral of motion results in relaxation to the quasi-thermodynamic equilibrium between parts of the system. The "temperature" of such state is determined by energy of the system and by the mean value of measured integral of motion. PACS numbers: 03.65.Ta, 05.40.-a