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Multiple-scale stochastic processes: Decimation, averaging and beyond
KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
2017 (English)In: Physics reports, ISSN 0370-1573, E-ISSN 1873-6270, Vol. 670, 1-59 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 670, 1-59 p.
Keyword [en]
Diffusive processes, Irreversibility, Markov processes, Multiscale methods, Stochastic functionals
National Category
Control Engineering Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-202162DOI: 10.1016/j.physrep.2016.12.003ISI: 000394409200001Scopus ID: 2-s2.0-85009513898OAI: oai:DiVA.org:kth-202162DiVA: diva2:1079292
Note

QC 20170308

Available from: 2017-03-08 Created: 2017-03-08 Last updated: 2017-03-20Bibliographically approved

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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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  • asciidoc
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