Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision of estimation to average dissipation. Here we consider this...
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| Format: | Article |
| Language: | English |
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American Physical Society
2017
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| Online Access: | https://eprints.nottingham.ac.uk/42408/ |
| _version_ | 1848796481094418432 |
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| author | Garrahan, Juan P. |
| author_facet | Garrahan, Juan P. |
| author_sort | Garrahan, Juan P. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision of estimation to average dissipation. Here we consider this problem but for counting observables, i.e., trajectory observables which, in contrast to currents, are non-negative and nondecreasing in time (and possibly symmetric under time reversal). In the steady state, their fluctuations to all orders are bound from below by a Conway-Maxwell-Poisson distribution dependent only on the averages of the observable and of the dynamical activity. We show how to obtain the corresponding bounds for first-passage times (times when a certain value of the counting variable is first reached) and their uncertainty relations. Just like entropy production does for currents, dynamical activity controls the bounds on fluctuations of counting observables. |
| first_indexed | 2025-11-14T19:48:40Z |
| format | Article |
| id | nottingham-42408 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T19:48:40Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-424082018-10-12T15:25:41Z https://eprints.nottingham.ac.uk/42408/ Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables Garrahan, Juan P. Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision of estimation to average dissipation. Here we consider this problem but for counting observables, i.e., trajectory observables which, in contrast to currents, are non-negative and nondecreasing in time (and possibly symmetric under time reversal). In the steady state, their fluctuations to all orders are bound from below by a Conway-Maxwell-Poisson distribution dependent only on the averages of the observable and of the dynamical activity. We show how to obtain the corresponding bounds for first-passage times (times when a certain value of the counting variable is first reached) and their uncertainty relations. Just like entropy production does for currents, dynamical activity controls the bounds on fluctuations of counting observables. American Physical Society 2017-03-23 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/42408/7/PhysRevE.95.032134.pdf Garrahan, Juan P. (2017) Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables. Physical Review E, 95 (3). 032134-1. ISSN 2470-0053 https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.032134 doi:10.1103/PhysRevE.95.032134 doi:10.1103/PhysRevE.95.032134 |
| spellingShingle | Garrahan, Juan P. Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables |
| title | Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables |
| title_full | Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables |
| title_fullStr | Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables |
| title_full_unstemmed | Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables |
| title_short | Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables |
| title_sort | simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables |
| url | https://eprints.nottingham.ac.uk/42408/ https://eprints.nottingham.ac.uk/42408/ https://eprints.nottingham.ac.uk/42408/ |