Experimental Measurement of Relative Path Probabilities and Stochastic Actions

For diffusive stochastic dynamics, the probability to observe any individual trajectory is vanishingly small, making it unclear how to experimentally validate theoretical results for ratios of path probabilities. We provide the missing link between theory and experiment by establishing a protocol to...

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Autores principales:	Jannes Gladrow, Ulrich F. Keyser, R. Adhikari, Julian Kappler
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/86fd7e96230a41febb06a078f0f906fb
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spelling	oai:doaj.org-article:86fd7e96230a41febb06a078f0f906fb2021-12-02T16:44:12ZExperimental Measurement of Relative Path Probabilities and Stochastic Actions10.1103/PhysRevX.11.0310222160-3308https://doaj.org/article/86fd7e96230a41febb06a078f0f906fb2021-07-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.031022http://doi.org/10.1103/PhysRevX.11.031022https://doaj.org/toc/2160-3308For diffusive stochastic dynamics, the probability to observe any individual trajectory is vanishingly small, making it unclear how to experimentally validate theoretical results for ratios of path probabilities. We provide the missing link between theory and experiment by establishing a protocol to extract ratios of path probabilities from measured time series. For experiments on a single colloidal particle in a microchannel, we extract both ratios of path probabilities and the most probable path for a barrier crossing, and find excellent agreement with independently calculated predictions based on the Onsager-Machlup stochastic action. Our experimental results at room temperature are found to be inconsistent with the low-noise Freidlin-Wentzell stochastic action, and we discuss under which circumstances the latter action is expected to describe the most probable path. Furthermore, while the experimentally accessible ratio of path probabilities is uniquely determined, the formal path-integral action is known to depend on the time-discretization scheme used for deriving it; we reconcile these two seemingly contradictory facts by careful analysis of the time-slicing derivation of the path integral. Our experimental protocol enables us to probe probability distributions on path space and allows us to relate theoretical single-trajectory results to measurement.Jannes GladrowUlrich F. KeyserR. AdhikariJulian KapplerAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 3, p 031022 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Jannes Gladrow Ulrich F. Keyser R. Adhikari Julian Kappler Experimental Measurement of Relative Path Probabilities and Stochastic Actions
description	For diffusive stochastic dynamics, the probability to observe any individual trajectory is vanishingly small, making it unclear how to experimentally validate theoretical results for ratios of path probabilities. We provide the missing link between theory and experiment by establishing a protocol to extract ratios of path probabilities from measured time series. For experiments on a single colloidal particle in a microchannel, we extract both ratios of path probabilities and the most probable path for a barrier crossing, and find excellent agreement with independently calculated predictions based on the Onsager-Machlup stochastic action. Our experimental results at room temperature are found to be inconsistent with the low-noise Freidlin-Wentzell stochastic action, and we discuss under which circumstances the latter action is expected to describe the most probable path. Furthermore, while the experimentally accessible ratio of path probabilities is uniquely determined, the formal path-integral action is known to depend on the time-discretization scheme used for deriving it; we reconcile these two seemingly contradictory facts by careful analysis of the time-slicing derivation of the path integral. Our experimental protocol enables us to probe probability distributions on path space and allows us to relate theoretical single-trajectory results to measurement.
format	article
author	Jannes Gladrow Ulrich F. Keyser R. Adhikari Julian Kappler
author_facet	Jannes Gladrow Ulrich F. Keyser R. Adhikari Julian Kappler
author_sort	Jannes Gladrow
title	Experimental Measurement of Relative Path Probabilities and Stochastic Actions
title_short	Experimental Measurement of Relative Path Probabilities and Stochastic Actions
title_full	Experimental Measurement of Relative Path Probabilities and Stochastic Actions
title_fullStr	Experimental Measurement of Relative Path Probabilities and Stochastic Actions
title_full_unstemmed	Experimental Measurement of Relative Path Probabilities and Stochastic Actions
title_sort	experimental measurement of relative path probabilities and stochastic actions
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/86fd7e96230a41febb06a078f0f906fb
work_keys_str_mv	AT jannesgladrow experimentalmeasurementofrelativepathprobabilitiesandstochasticactions AT ulrichfkeyser experimentalmeasurementofrelativepathprobabilitiesandstochasticactions AT radhikari experimentalmeasurementofrelativepathprobabilitiesandstochasticactions AT juliankappler experimentalmeasurementofrelativepathprobabilitiesandstochasticactions
_version_	1718383526097715200

Experimental Measurement of Relative Path Probabilities and Stochastic Actions

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