Edinburgh Research Explorer

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

Research output: Contribution to journalArticlepeer-review

Related Edinburgh Organisations

Open Access permissions



Original languageEnglish
Number of pages31
JournalJournal of Physics A: Mathematical and Theoretical
Publication statusPublished - 26 Sep 2019


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.

    Research areas

  • cond-mat.stat-mech

Download statistics

No data available

ID: 110657195