A numerical approach to large deviations in continuous time

Vivien Lecomte (1, 2) , Julien Tailleur (3)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
2 MSC - Matière et Systèmes Complexes
3 PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)

We present an algorithm to evaluate large deviation functions associated to history-dependent observables. Instead of relying on a time discretization procedure to approximate the dynamics, we provide a direct continuous-time algorithm valuable for systems with multiple timescales, thus extending the work of Giardinà, Kurchan and Peliti (2006 Phys. Rev. Lett. 96 120603). The procedure is supplemented with a thermodynamic-integration scheme which improves its efficiency. We also show how the method can be used to probe large deviation functions in systems with a dynamical phase transition—revealed in our context through the appearance of a non-analyticity in the large deviation functions.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Vivien Lecomte, Julien Tailleur. A numerical approach to large deviations in continuous time. Journal of Statistical Mechanics: Theory and Experiment, 2007, pp.P03004. ⟨10.1088/1742-5468/2007/03/P03004⟩. ⟨hal-00160784⟩