On Lossless Approximations, the Fluctuation-Dissipation Theorem, and Limitations of Measurements

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On Lossless Approximations, the Fluctuation-Dissipation Theorem, and Limitations of Measurements

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Title: On Lossless Approximations, the Fluctuation-Dissipation Theorem, and Limitations of Measurements
Author: Sandberg, Henrik; Delvenne, Jean-Charles; Doyle, John M.

Note: Order does not necessarily reflect citation order of authors.

Citation: Sandberg, Henrik, Delvenne, Jean-Charles, and John Doyle. 2011. On lossless approximations, the fluctuation-dissipation theorem, and limitations of measurements. IEEE Transactions on Automatic Control 56(2): 293 - 308.
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Abstract: In this paper, we take a control-theoretic approach to answering some standard questions in statistical mechanics, and use the results to derive limitations of classical measurements. A central problem is the relation between systems which appear macroscopically dissipative but are microscopically lossless. We show that a linear system is dissipative if, and only if, it can be approximated by a linear lossless system over arbitrarily long time intervals. Hence lossless systems are in this sense dense in dissipative systems. A linear active system can be approximated by a nonlinear lossless system that is charged with initial energy. As a by-product, we obtain mechanisms explaining the Onsager relations from time-reversible lossless approximations, and the fluctuation-dissipation theorem from uncertainty in the initial state of the lossless system. The results are applied to measurement devices and are used to quantify limits on the so-called observer effect, also called back action, which is the impact the measurement device has on the observed system. In particular, it is shown that deterministic back action can be compensated by using active elements, whereas stochastic back action is unavoidable and depends on the temperature of the measurement device.
Published Version: doi:10.1109/TAC.2010.2056450
Other Sources: http://arxiv.org/abs/1009.2830v1
Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:8866875

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  • FAS Scholarly Articles [7220]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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