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Mapping out of equilibrium into equilibrium in one-dimensional transport models | Julien Tailleur
; Jorge Kurchan
; Vivien Lecomte
; | Date: |
3 Sep 2008 | Abstract: | Systems with conserved currents driven by reservoirs at the boundaries offer
an opportunity for a general analytic study that is unparalleled in more
general out of equilibrium systems. The evolution of coarse-grained variables
is governed by stochastic {em hydrodynamic} equations in the limit of small
noise.} As such it is amenable to a treatment formally equal to the
semiclassical limit of quantum mechanics, which reduces the problem of finding
the full distribution functions to the solution of a set of Hamiltonian
equations. It is in general not possible to solve such equations explicitly,
but for an interesting set of problems (driven Symmetric Exclusion Process and
Kipnis-Marchioro-Presutti model) it can be done by a sequence of remarkable
changes of variables. We show that at the bottom of this ’miracle’ is the
surprising fact that these models can be taken through a non-local
transformation into isolated systems satisfying detailed balance, with
probability distribution given by the Gibbs-Boltzmann measure. This procedure
can in fact also be used to obtain an elegant solution of the much simpler
problem of non-interacting particles diffusing in a one-dimensional potential,
again using a transformation that maps the driven problem into an undriven one. | Source: | arXiv, 0809.0709 | Services: | Forum | Review | PDF | Favorites |
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