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Driven nonequilibrium systems modeled with Markov processes
Thesis (PhD)--Stellenbosch University, 2017
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2017
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| _version_ | 1867613851183218688 |
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| access_status_str | Open Access |
| author | Nyawo, Pelerine Tsobgni |
| author2 | Touchette, Hugo |
| author_browse | Nyawo, Pelerine Tsobgni Touchette, Hugo |
| author_facet | Touchette, Hugo Nyawo, Pelerine Tsobgni |
| author_sort | Nyawo, Pelerine Tsobgni |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2017 |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/102761 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:42:41.823Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2017 |
| publishDateRange | 2017 |
| publishDateSort | 2017 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/102761 Driven nonequilibrium systems modeled with Markov processes Nyawo, Pelerine Tsobgni Touchette, Hugo Kastner, Michael Stellenbosch University. Faculty of Science. Dept. of Physics. Nonequilibrium systems Markov processes Time-integrated functionals Periodic diffusion Thesis (PhD)--Stellenbosch University, 2017 ENGLISH ABSTRACT : We study in this thesis the fluctuations of time-integrated functionals of Markov processes, which represent physical observables that can be measured in time for noisy systems driven in nonequilibrium steady states. The goal of the thesis is to illustrate how techniques from the theory of large deviations can be used to obtain the probability distribution of these observables in the long-time limit through the knowledge of an important function, called the rate function. We also illustrate in this thesis a recent theory of driven processes that aims to describe how fluctuations of observables are created in time by means of an effective process with modified forces or potentials. This is done by studying two simple models of nonequilibrium processes based on the Langevin equation. The first is a periodic diffusion that has current fluctuations, whereas the second is the simple drifted Brownian motion for which we study the occupation fluctuations. For these two models, we calculate analytically and numerically the rate function, as well as the associated driven process. The results for the periodic diffusion show, on the one hand, that there is a Gaussian to non-Gaussian crossover in the current fluctuations, which can easily be interpreted from the form of the driven process. On the other hand, the Brownian model provides one of the simplest examples of a dynamical phase transition, that is, a phase transition in the fluctuations of observables. Other connections with fluctuation relations, Josephson junctions, and the geometric Brownian motion are discussed. AFRIKAANSE OPSOMMING : Ons bestudeer in hierdie tesis die fluktuasies van tyd-geïntegreerde funksionele van Markov prosesse, wat fisiese waarneembares wat in tyd gemeet kan word verteenwoordig vir stelses met geraas en wat gedryf word tot nieewewig bestendige state. Die doel van hierdie tesis is om te illustreer hoe tegnieke van die teorie van groot fluktuasies gebruik kan word om die waarskynlikheidsverspreiding van hierdie waarneembares in die lang-tyd limiet te bepaal deur kennis van ’n belangrike funksie, die sogenaamde koers funksie, te gebruik. Ons illustreer ook in hierdie tesis ’n onlangse teorie van gedrewe prosesse wat daarop gemik is om te beskryf hoe fluktuasies van waarneembares geskep word in tyd deur middel van ’n effektiewe proses met gewysigde kragte of potensiale. Hierdie word gedoen deur twee eenvoudige nie-ewewig prosesse wat op die Langevin-vergelyking gebaseer is te bestudeer. Die eerste proses is a periodieke diffusie wat stroom fluktuasies bevat, terwyl die tweede proses ’n eevoudige Browniese beweging met drif is waarvoor ons die besettings fluktuasies bestudeer. Vir hierdie twee modelle bereken ons analities en numeries die koers funksie asook die geassosieerde gedrewe proses. Die resultate vir die periodieke diffusie wys, aan die een kant, dat daar ’n oorkruising vanaf Gaussiese tot nie-Gaussiese stroom fluktuasies bestaan, wat maklik vanuit die vorm van die gedrewe proses geïnterpreteer kan word. Aan die ander kant verskaf die Browniese model die eenvoudigste voorbeeld van ’n dinamiese fase oorgang, dit wil sê, ’n oorgang in die fluktuasies van waarneembares. Ander verbindinge met fluktuasieverhoudinge, Josephson-kruisings en die geometriese Browniese beweging word bespreek. Doctoral 2017-11-08T12:05:27Z 2017-12-11T10:51:01Z 2017-11-08T12:05:27Z 2017-12-11T10:51:01Z 2017-12 Thesis http://hdl.handle.net/10019.1/102761 en_ZA Stellenbosch University xii, 84 pages : illustrations (some colour) application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Nonequilibrium systems Markov processes Time-integrated functionals Periodic diffusion Nyawo, Pelerine Tsobgni Driven nonequilibrium systems modeled with Markov processes |
| title | Driven nonequilibrium systems modeled with Markov processes |
| title_full | Driven nonequilibrium systems modeled with Markov processes |
| title_fullStr | Driven nonequilibrium systems modeled with Markov processes |
| title_full_unstemmed | Driven nonequilibrium systems modeled with Markov processes |
| title_short | Driven nonequilibrium systems modeled with Markov processes |
| title_sort | driven nonequilibrium systems modeled with markov processes |
| topic | Nonequilibrium systems Markov processes Time-integrated functionals Periodic diffusion |
| url | http://hdl.handle.net/10019.1/102761 |
| work_keys_str_mv | AT nyawopelerinetsobgni drivennonequilibriumsystemsmodeledwithmarkovprocesses |