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

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

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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.

Item Type: Article
Keywords: large deviations in non-equilibrium systems, dynamical processes, fluctuation phenomena, current fluctuations
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Physics and Astronomy
Identification Number: 10.1088/1742-5468/2016/07/073208
Depositing User: Eprints, Support
Date Deposited: 05 Jan 2017 09:41
Last Modified: 18 Oct 2017 18:34
URI: http://eprints.nottingham.ac.uk/id/eprint/39590

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