Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles
Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles
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DOI：
10.1088/1742-5468/2016/07/073208
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发表时间：
2016-07-01
影响因子：
2.4
通讯作者：
Garrahan, Juan P.
中科院分区：
文献类型：
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作者：
Garrahan, Juan P.
借鉴开放量子系统的思想，我们描述了一种用连续矩阵积态(CMPS)来编码经典随机动力学轨迹系综的形式。我们展示了如何在这种方法中定义“有偏的”或“有条件的”系综，在这些系综中，轨道的概率与自然动力学的概率因轨道可观测的某些条件而有偏差。特别地，我们证明了将条件过程映射到等价的‘辅助’或‘驱动’过程的广义Doob变换(其中相同的条件轨道集是由适当的随机动力学产生的)仅仅是相应CMPS的规范变换。我们还讨论了如何在这个框架内很容易地证明动力学的性质，如轨道系综等价和涨落定理。
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.