Effective stochastic generators for conditioned dynamics at an atypical reaction-diffusion current
Effective stochastic generators for conditioned dynamics at an atypical reaction-diffusion current
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DOI：
10.1103/physreve.92.062104
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发表时间：
2015-12-02
影响因子：
2.4
通讯作者：
Jafarpour, Farhad H.
中科院分区：
文献类型：
--
作者：
Torkaman, Pegah;Jafarpour, Farhad H.
我们考虑一般随机马尔可夫过程中时间积分粒子电流围绕非典型值的波动，该过程涉及具有开放边界的有限一维晶格上具有两位点相互作用和硬核排斥的经典粒子。我们解决的问题是，人们必须在这一过程中施加哪些互动，才能使当前的非典型价值变得典型。已知在时间平移不变区内可能存在相应的有效随机马尔可夫过程，其典型电流值等于原始过程中的非典型电流值。原则上，这个有效的过程具有非本地转移率。然而，事实证明，在某些条件下，有效过程的随机生成器与原始过程的随机生成器具有相同的动力学规则。我们发现了这些条件并表明我们的方法可以推广到任何时间积分可观测值。
We consider the fluctuations of a time-integrated particle current around an atypical value in a generic stochastic Markov process involving classical particles with two-site interaction and hard-core repulsion on a finite one-dimensional lattice with open boundaries. We address the question of which interactions one has to impose on such a process to make the atypical value of the current typical. It is known that a corresponding effective stochastic Markov process might exist whose typical current value is equal to the atypical current value in the original process within a time-translational invariant regime. This effective process has, in principle, nonlocal transition rates. Nevertheless, it turns out that under some conditions, the stochastic generator of the effective process has the same dynamical rules as the stochastic generator of the original process. We find these conditions and show that our approach can be generalized to any time-integrated observable.