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Article overview
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Classical stochastic dynamics and continuous matrix product states: gauge transitions, conditioned and driven processes, and equivalence of trajectory ensembles | | Juan P. Garrahan
; | | Date: |
25 Feb 2016 | | 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 (cMPS). 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. | | Source: | arXiv, 1602.7966 | | Services: | Forum | Review | PDF | Favorites | |
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