While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution.

\r\n\r\nMotivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.

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San Diego, CA: Academic Press, 2004" ] }, "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "collection": "CaltechTHESIS", "reviewer": "Kathy Johnson", "deposited_by": "Aristotelis Asimakopoulos", "deposited_on": "2014-09-25 17:08:00", "doi": "10.7907/Z9V40S4N", "divisions": { "items": [ "div_eng" ] }, "institution": "California Institute of Technology", "thesis_type": "phd", "thesis_advisor": { "items": [ { "email": "doyle@cds.caltech.edu", "id": "Doyle-J-C", "name": { "family": "Doyle", "given": "John Comstock" }, "role": "advisor" } ] }, "thesis_committee": { "items": [ { "email": "hajimiri@caltech.edu", "id": "Hajimiri-A", "name": { "family": "Hajimiri", "given": "Ali" }, "role": "chair" }, { "email": "phillips@pboc.caltech.edu", "id": "Phillips-R-B", "name": { "family": "Phillips", "given": "Robert B." }, "role": "member" }, { "email": "mani@cs.caltech.edu", "id": "Chandy-K-M", "name": { "family": "Chandy", "given": "K. Mani" }, "role": "member" }, { "email": "doyle@cds.caltech.edu", "id": "Doyle-J-C", "name": { "family": "Doyle", "given": "John Comstock" }, "role": "member" } ] }, "thesis_degree": "PHD", "thesis_degree_grantor": "California Institute of Technology", "thesis_defense_date": "2014-06-08", "gradofc_approval_date": "2014-09-24", "review_status": "approved", "option_major": { "items": [ "eleceng" ] }, "copyright_statement": "Author's Rights Authorization: I hereby certify that, if appropriate, I have obtained a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted here is the same as that approved by my advisory committee.\n\nI hereby grant to California Institute of Technology or its agents the non-exclusive license to archive and make accessible, under the conditions specified under \"Thesis Availability\" in this submission, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation, or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.", "resource_type": "thesis", "pub_year": "2015", "author_list": "Asimakopoulos, Aristotelis" } ]