Living on the edge of instability
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10405369" target="_blank" >RIV/00216208:11320/19:10405369 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wxr0mJIjeX" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wxr0mJIjeX</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1742-5468/ab333f" target="_blank" >10.1088/1742-5468/ab333f</a>
Alternative languages
Result language
angličtina
Original language name
Living on the edge of instability
Original language description
Statistical description of stochastic dynamics in highly unstable potentials is strongly affected by properties of divergent trajectories, that quickly leave meta-stable regions of the potential landscape and never return. Using ideas from theory of Q-processes and quasi-stationary distributions, we analyze position statistics of non-diverging trajectories. We discuss two limit distributions which can be considered as (formal) generalizations of the Gibbs canonical distribution to highly unstable systems. Even though the associated effective potentials differ only slightly, properties of the two distributions are fundamentally different for all highly unstable system. The distribution for trajectories conditioned to diverge in an infinitely distant future is localized and light-tailed. The other distribution, describing trajectories surviving in the meta-stable region at the instant of conditioning, is heavy-tailed. The exponent of the corresponding power-law tail is determined by the leading divergent term of the unstable potential. We discuss different equivalent forms of the two distributions and derive properties of the effective statistical force arising in the ensemble of non-diverging trajectories after the Doob h-transform. The obtained explicit results generically apply to non-linear dynamical models with meta-stable states and fast kinetic transitions.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10300 - Physical sciences
Result continuities
Project
<a href="/en/project/GA17-06716S" target="_blank" >GA17-06716S: Stochastic thermodynamics of molecular systems: from classical to quantum</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Statistical Mechanics: Theory and Experiment
ISSN
1742-5468
e-ISSN
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Volume of the periodical
Neuveden
Issue of the periodical within the volume
August 2019
Country of publishing house
GB - UNITED KINGDOM
Number of pages
18
Pages from-to
084014
UT code for WoS article
000482548900003
EID of the result in the Scopus database
2-s2.0-85072301090