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Published 2007 | Published
Book Section - Chapter Open

The Statistical Mechanics of Fluctuation-Dissipation and Measurement Back Action

Abstract

In this paper, we take a control-theoretic approach to answering some standard questions in statistical mechanics. A central problem is the relation between systems which appear macroscopically dissipative but are microscopically lossless. We show that a linear macroscopic system is dissipative if and only if it can be approximated by a linear lossless microscopic system, over arbitrarily long time intervals. As a by-product, we obtain mechanisms explaining Johnson-Nyquist noise as initial uncertainty in the lossless state, as well as measurement back action and a trade-off between process and measurement noise.

Additional Information

© 2007 IEEE. Issue Date: 9-13 July 2007; Date of Current Version: 30 July 2007. H. Sandberg is supported by the Hans Werthén foundation and a postdoctoral grant from the Swedish Research Council. This research was partly supported by the FNRS and the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office. The scientific responsibility rests with its authors. The authors would like to thank Ben Recht for many helpful suggestions and comments.

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Created:
August 19, 2023
Modified:
January 13, 2024