Effective stochastic generators for conditioned dynamics at an atypical reaction-diffusion current

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Pegah Torkaman, Farhad H Jafarpour

Abstract

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.

References

Jun 1, 2004·Physical Review Letters·R M L Evans
Jul 21, 2006·The Journal of Physical Chemistry. B·Weinan EEric Vanden-Eijnden
Nov 1, 2006·Proceedings of the National Academy of Sciences of the United States of America·George D RoseAmos Maritan
Dec 31, 2008·Physical Review Letters·A Baule, R M L Evans
Feb 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pegah Torkaman, Farhad H Jafarpour

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Citations

May 24, 2017·Physical Biology·Jordan M Horowitz, Rahul V Kulkarni
Jan 5, 2019·Physical Biology·Niraj Kumar, Rahul V Kulkarni
Aug 29, 2019·Physical Biology·Pegah Torkaman, Farhad H Jafarpour

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