Character of fluctuations in deterministically thermostatted nonequilibrium systems.

The application of Nose-Hoover equations of motion to analysis of stationary nonequilibrium systems-driven away from equilibrium by inherent thermostatting-is briefly discussed. The Galton board model, to which the analysis does apply, is described. Numerical simulations of this specific model suggest that the system exhibits 1/f(k) noise, with 1</=k</=2. Explanation of this property is based on the fact that the system approaches an ergodic strange attractor due to the action of inherent friction force. Analysis of generalized baker maps which also have strange attractors but exhibit white noise, is used to support the view that the presence of strange attractor alone is not sufficient for appearance of 1/f noise. It seems that the latter is found only in thermostatted systems which without thermostatting have 1/f(2) noise. The paper concludes with the discussion of many open problems which still remain unsolved in this approach. (c) 2001 American Institute of Physics.