On Lossless Approximations, the Fluctuation-Dissipation Theorem, and Limitations of Measurements
2011 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 56, no 2, 293-308 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
IEEE , 2011. Vol. 56, no 2, 293-308 p.
Dissipative systems, fluctuation-dissipation theorem, fundamental limits, lossless systems, micro-electro-mechanical systems (MEMS), observer effect, statistical mechanics
IdentifiersURN: urn:nbn:se:kth:diva-31007DOI: 10.1109/TAC.2010.2056450ISI: 000287084300005ScopusID: 2-s2.0-79951617721OAI: oai:DiVA.org:kth-31007DiVA: diva2:404794
FunderSwedish Research Council, 2007-6350Swedish Research Council, 2009-4565ICT - The Next Generation
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QC 201103182012-02-142011-03-072012-02-14Bibliographically approved