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Nonequilibrium Statistical Models: Guided Network Growth Under Localized Information and Perspectives on Electron Diffusion in Conductors

The ability to probe many-particle systems on a microscopic level has revolutionized the

way we do statistical physics. As computational capabilities continue to grow exponentially, larger

and more complex systems come within reach of microscopic analysis. In the field of network

growth, the classical model has given way to competitive processes, in which networks are guided

by some criteria at every step of their formation. We develop and analyze a new competitive

growth process that permits intervention on growing networks using only local properties of the

network when evaluating how to add new connections. We establish the critical behavior of this

new method and explore potential uses in guiding the development of real-world networks.

The classical system of electrons diffusing within a conductor similarly permits a

microscopic analysis where, to date, studies of the macroscopic properties have dominated the

literature. In order to extend our understanding of the theory that governs this diffusion—the

fluctuation-dissipation theorem—we construct a physical model of the Johnson-Nyquist system

of electrons embedded in the bulk of a conductor. Constructing the model involves deriving how

the motion of each individual electron comes about via scattering processes in the conductor, then

connecting this collective motion to the macroscopic observables of voltage and current that define

Johnson-Nyquist noise. Once the equilibrium properties have been fully realized, an external

perturbation can be applied in order to probe the behavior of the model as it deviates away from

equilibrium. In much the same way that competitive network growth revolutionized classical

network theory, we aim to establish a model which can guide future research into nonequilibrium

fluctuation-dissipation by providing a method for interacting with the system in a precise and

well-controlled manner as it evolves over time. This model is presented in its present form in

Chapter 3.

Chapter 2, which covers this work, has been published in Physical Review E as a Rapid

Communication [1]. The writing and analysis were performed by me as the primary author. Eric

Corwin and Georgios Tsekenis are listed as co-authors for their contribution to the analysis and

for advisement on the work.

This dissertation includes previously published and unpublished co-authored material.

Identiferoai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/23915
Date31 October 2018
CreatorsTrevelyan, Alexander
ContributorsCorwin, Eric
PublisherUniversity of Oregon
Source SetsUniversity of Oregon
Languageen_US
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
RightsAll Rights Reserved.

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