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

TL;DR

This paper introduces a modified quantum measurement theory for classical open systems, describing how measurements influence system evolution via a specialized Fokker-Planck equation, and explores measurement-induced stationary states and quasi-thermodynamic equilibria.

Contribution

It presents a novel approach linking quantum measurement theory to classical open systems using a unique Fokker-Planck framework, and analyzes measurement-induced stationary states.

Findings

Measurement affects the evolution of classical open systems via a specific Fokker-Planck equation.

Measurement of conserved quantities can induce relaxation to quasi-thermodynamic states.

The 'temperature' of measurement-induced states depends on system energy and measured quantities.

Abstract

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