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Extreme current fluctuations of boundary-driven systems in the large-N limit | | Yongjoo Baek
; Yariv Kafri
; Vivien Lecomte
; | | Date: |
23 Feb 2016 | | Abstract: | Current fluctuations in boundary-driven diffusive systems are, in many cases,
studied using hydrodynamic theories. Their predictions are then expected to be
valid for currents which scale inversely with the system size. To study this
question in detail, we introduce a class of large-N models of one-dimensional
boundary-driven diffusive systems, whose current large deviation functions are
exactly derivable. Surprisingly, we find that for some systems the predictions
of the hydrodynamic theory may hold well beyond their naive regime of validity.
Specifically, we show that, while a symmetric partial exclusion process
exhibits non-hydrodynamic behaviors sufficiently far beyond the naive
hydrodynamic regime, a symmetric inclusion process is well described by the
hydrodynamic theory for arbitrarily large currents. We conjecture, and verify
for zero-range processes, that the hydrodynamic theory captures the statistics
of arbitrarily large currents for all models where the mobility coefficient as
a function of density is unbounded from above. In addition, for the large-N
models, we prove the additivity principle under the assumption that the large
deviation function has no discontinuous transitions. | | Source: | arXiv, 1602.7155 | | Services: | Forum | Review | PDF | Favorites | |
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