FisMat2017 - Submission - View

Abstract's title: First-order transitions in the Large Deviations of non-interacting Run-and-Tumble particles
Submitting author: Giacomo Gradenigo
Affiliation: LIPhy- Université Grenoble-Alpes
Affiliation Address: Grenoble
Country: France
Oral presentation/Poster (Author's request): Oral presentation
Other authors and affiliations: Satya N. Majumdar (LPTMS, Université Paris-Sud, Orsay)
We present here analytical arguments and the numerical evidence that the condensation transition observed for the probability distribution P(X,N) of the displacement along a trajectory of non-interacting Run-and-Tumble particles in one dimension is related to non-analyticities of the rate function \Phi(x) for the Large Deviations. In particular we show that the condensation of fluctuations is related to a discontinuity of the first-order derivative of the rate function, both in presence of a finite acceleration for the particles and for free RTPs. The rate function plays the role of the free energy when the condensation of fluctuations is regarded as a dynamical phase-transition in the space of trajectories: our main result is therefore the evidence of the first-order character of this transition. We also comment on the interplay between the Fluctuation Relation and non-uniform Large Deviations when the Run-and-Tumble particles are accelerated by the external uniform field.