Journal of Statistical Mechanics: Theory and Experiment
Volume 2007
March 2007
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Vivien Lecomte and Julien Tailleur J. Stat. Mech. (2007) P03004 doi:10.1088/1742-5468/2007/03/P03004
A numerical approach to large deviations in continuous time
Vivien Lecomte1,2 and Julien Tailleur3
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| Figure 1. A history of the system between time t0 = 0 and time t. |
| Figure 2. Numerical evaluation of (1/L)ψQ(s) for the Simple Exclusion Process (N = 200, L = 400). (a) Comparison between direct numerical measurement (blue crosses) and results from thermodynamic integration (red circles). (b) Comparison between numerical results (red circles) and analytical prediction (22) valid for small s (blue line). |
Figure 3. Plot of the large deviation function
(1/L)ψQ(s) of the asymmetric simple exclusion process, for
L = 400 sites and
N = 200 particles. The jump rates are p = 1.2 and q = 0.8, whence  . Blue crosses and red circles correspond to direct computation and thermodynamic integration, respectively. The asymmetry appears when comparing the extreme points
s = ± 9.5. |
Figure 4. (a) Average profile ρ for s = 0.3. To minimize the overall current, the system develops an asymmetric shock, where only the front particles can jump easily. (b) A typical configuration for  . The particles are distributed almost uniformly. Note that  with s < 0 gives a similar result. |
Figure 5. (a) Plot of the large deviation function
(1/L)ψK(s) associated to the number of events K in the contact process in a field (L = 120 sites). (b) The dynamical phase transition occurs at
sc ~ 0.057. This is exemplified by plotting  for different system sizes (L = 4 in black, 8 in red, 15 in blue and 50 in magenta). |
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