Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles

Garrahan, Juan P.

Abstract

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.

Citation

Garrahan, J. 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), Article 073208. https://doi.org/10.1088/1742-5468/2016/07/073208

• Journal Article Type: Article
• Acceptance Date: Jun 23, 2016
• Publication Date: Jul 26, 2016
• Deposit Date: Jan 5, 2017
• Publicly Available Date: Jan 5, 2017
• Journal: Journal of Statistical Mechanics: Theory and Experiment
• Electronic ISSN: 1742-5468
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 2016
• Issue: 7
• Article Number: 073208
• DOI: https://doi.org/10.1088/1742-5468/2016/07/073208
• Keywords: large deviations in non-equilibrium systems, dynamical processes, fluctuation phenomena, current fluctuations
• Public URL: https://nottingham-repository.worktribe.com/output/799409
• Publisher URL: http://iopscience.iop.org/article/10.1088/1742-5468/2016/07/073208/
• Contract Date: Jan 5, 2017