Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles
Borrowing ideas from open quantum systems, we describe a formalism to encode ensembles of trajectories of classical stochastic dynamics in terms of continuous matrix product states (cMPSs). We show how to define in this approach 'biased' or 'conditioned' ensembles where the proba...
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| Format: | Article |
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IOP Publishing
2016
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| Online Access: | https://eprints.nottingham.ac.uk/39590/ |
| _version_ | 1848795871629541376 |
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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 | Borrowing ideas from open quantum systems, we describe a formalism to encode ensembles of trajectories of classical stochastic dynamics in terms of continuous matrix product states (cMPSs). We show how to define in this approach 'biased' or 'conditioned' ensembles where the probability of trajectories is biased from that of the natural dynamics by some condition on trajectory observables. In particular, we show that the generalised Doob transform which maps a conditioned process to an equivalent 'auxiliary' or 'driven' process (one where the same conditioned set of trajectories is generated by a proper stochastic dynamics) is just a gauge transformation of the corresponding cMPS. We also discuss how within this framework one can easily prove properties of the dynamics such as trajectory ensemble equivalence and fluctuation theorems. |
| first_indexed | 2025-11-14T19:38:59Z |
| format | Article |
| id | nottingham-39590 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:38:59Z |
| publishDate | 2016 |
| publisher | IOP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-395902020-05-04T17:59:35Z https://eprints.nottingham.ac.uk/39590/ Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles Garrahan, Juan P. Borrowing ideas from open quantum systems, we describe a formalism to encode ensembles of trajectories of classical stochastic dynamics in terms of continuous matrix product states (cMPSs). We show how to define in this approach 'biased' or 'conditioned' ensembles where the probability of trajectories is biased from that of the natural dynamics by some condition on trajectory observables. In particular, we show that the generalised Doob transform which maps a conditioned process to an equivalent 'auxiliary' or 'driven' process (one where the same conditioned set of trajectories is generated by a proper stochastic dynamics) is just a gauge transformation of the corresponding cMPS. We also discuss how within this framework one can easily prove properties of the dynamics such as trajectory ensemble equivalence and fluctuation theorems. IOP Publishing 2016-07-26 Article PeerReviewed Garrahan, Juan P. (2016) Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles. Journal of Statistical Mechanics: Theory and Experiment, 2016 (7). 073208/1-073208/22. ISSN 1742-5468 large deviations in non-equilibrium systems dynamical processes fluctuation phenomena current fluctuations http://iopscience.iop.org/article/10.1088/1742-5468/2016/07/073208/ doi:10.1088/1742-5468/2016/07/073208 doi:10.1088/1742-5468/2016/07/073208 |
| spellingShingle | large deviations in non-equilibrium systems dynamical processes fluctuation phenomena current fluctuations Garrahan, Juan P. Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles |
| title | Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles |
| title_full | Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles |
| title_fullStr | Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles |
| title_full_unstemmed | Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles |
| title_short | Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles |
| title_sort | classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles |
| topic | large deviations in non-equilibrium systems dynamical processes fluctuation phenomena current fluctuations |
| url | https://eprints.nottingham.ac.uk/39590/ https://eprints.nottingham.ac.uk/39590/ https://eprints.nottingham.ac.uk/39590/ |