## Abstract

Suppose that a point-like steady source at x=0 injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the particles are non-interacting, their total number N in the steady state is Poisson-distributed with mean predicted from a deterministic reaction-diffusion equation. Here we determine the most likely density history of this driven system conditional on observing a given N. We also consider two prototypical examples of interacting diffusing particles: (i) a family of mortal diffusive lattice gases with constant diffusivity (as illustrated by the simple symmetric exclusion process with mortal particles), and (ii) random walkers that can annihilate in pairs. In both examples we calculate the variances of the (non-Poissonian) stationary distributions of N.

Original language | American English |
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Article number | P05004 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2015 |

Issue number | 5 |

DOIs | |

State | Published - 8 May 2015 |

### Bibliographical note

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

## Keywords

- Driven diffusive systems (theory)
- Large deviations in non-equilibrium systems
- Stochastic particle dynamics (theory)