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arXiv · 1905.10260

A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension

Emil Mallmin·Richard A Blythe·Martin R Evans
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Abstract

We compare the fluctuations in the velocity and in the fraction of time spent at a given position for minimal models of a passive and an active particle: an asymmetric random walker and a run-and-tumble particle in continuous time and on a 1D lattice. We compute rate functions and effective dynamics conditioned on large deviations for these observables. While generally different, for a unique and non-trivial choice of rates (up to a rescaling of time) the velocity rate functions for the two models become identical, whereas the effective processes generating the fluctuations remain distinct. This equivalence coincides with a remarkable parity of the spectra of the processes' generators. For the occupation-time problem, we show that both the passive and active particles undergo a prototypical dynamical phase transition when the average velocity is non-vanishing in the long-time limit.

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Emil Mallmin, Richard A Blythe, Martin R Evans. 2019-05-24. A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension. https://doi.org/10.1088/1751-8121%2Fab4349

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