## Abstract

Suppose that an infinite lattice gas of constant density n_{0}, whose dynamics are described by the symmetric simple exclusion process, is brought in contact with a spherical absorber of radius R. Employing the macroscopic fluctuation theory and assuming the additivity principle, we evaluate the probability distribution that N particles are absorbed during a long time T. The limit of N = 0 corresponds to the survival problem, whereas describes the opposite extreme. Here is the average number of absorbed particles (in three dimensions), and D_{0} is the gas diffusivity. For n_{0} 蠐 1 the exclusion effects are negligible, and can be approximated, for not too large N, by the Poisson distribution with mean . For finite n_{0}, is non-Poissonian. We show that at . At sufficiently large N and n_{0} < 1/2 the most likely density profile of the gas, conditional on the absorption of N particles, is non-monotonic in space. We also establish a close connection between this problem and that of statistics of current in finite open systems.

Original language | American English |
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Article number | P04009 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2015 |

Issue number | 4 |

DOIs | |

State | Published - 27 Apr 2015 |

### Bibliographical note

Publisher Copyright:© 2015 IOP Publishing Ltd and SISSA Medialab srl.

## Keywords

- current fluctuations
- large deviations in non-equilibrium systems
- stochastic particle dynamics (theory)