Multiple-scale stochastic processes: Decimation, averaging and beyond

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Bo, StefanoStockholms universitet,KTH,Nordic Institute for Theoretical Physics NORDITA,Nordiska institutet för teoretisk fysik (Nordita) (author)

Multiple-scale stochastic processes : Decimation, averaging and beyond

Article/chapterEnglish2017

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Elsevier,2017
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LIBRIS-ID:oai:DiVA.org:kth-202162
https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-202162URI
https://doi.org/10.1016/j.physrep.2016.12.003DOI
https://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-141431URI

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Language:English
Summary in:English

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QC 20170308
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This has provided fruitful applications for established stochastic methods and motivated further developments. These systems often involve processes taking place on widely separated time scales. For an efficient modeling one usually focuses on the slower degrees of freedom and it is of great importance to accurately eliminate the fast variables in a controlled fashion, carefully accounting for their net effect on the slower dynamics. This procedure in general requires to perform two different operations: decimation and coarse-graining. We introduce the asymptotic methods that form the basis of this procedure and discuss their application to a series of physical, biological and chemical examples. We then turn our attention to functionals of the stochastic trajectories such as residence times, counting statistics, fluxes, entropy production, etc. which have been increasingly studied in recent years. For such functionals, the elimination of the fast degrees of freedom can present additional difficulties and naive procedures can lead to blatantly inconsistent results. Homogenization techniques for functionals are less covered in the literature and we will pedagogically present them here, as natural extensions of the ones employed for the trajectories. We will also discuss recent applications of these techniques to the thermodynamics of small systems and their interpretation in terms of information-theoretic concepts.

Subject headings and genre

TEKNIK OCH TEKNOLOGIER Elektroteknik och elektronik Reglerteknik hsv//swe
ENGINEERING AND TECHNOLOGY Electrical Engineering, Electronic Engineering, Information Engineering Control Engineering hsv//eng
NATURVETENSKAP Data- och informationsvetenskap Datavetenskap hsv//swe
NATURAL SCIENCES Computer and Information Sciences Computer Sciences hsv//eng
NATURVETENSKAP Fysik hsv//swe
NATURAL SCIENCES Physical Sciences hsv//eng
Diffusive processes
Irreversibility
Markov processes
Multiscale methods
Stochastic functionals

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Celani, A. (author)
KTHNordic Institute for Theoretical Physics NORDITA (creator_code:org_t)

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In:Physics reports: Elsevier670, s. 1-590370-15731873-6270

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By the author/editor: Bo, Stefano; Celani, A.

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ENGINEERING AND TECHNOLOGY: ENGINEERING AND ...; and Electrical Engin ...; and Control Engineer ...

NATURAL SCIENCES: NATURAL SCIENCES; and Computer and Inf ...; and Computer Science ...

NATURAL SCIENCES: NATURAL SCIENCES; and Physical Science ...

Articles in the publication: Physics reports

By the university: Royal Institute of Technology; Stockholm University

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