The fluctuations of out of equilibrium systems are much richer
than those of equilibrium ones because time-reversibility is lost, and the Gibbs-Boltzmann distribution does not hold.
A general theory for large, smooth (`hydrodynamic') deviations has been developed in the last few years: it offers us a glimpse of what an out of equilibrium thermodynamics might one day look like.
When applied to several simple yet non-trivial one-dimensional transport models, it was found that a complete
analytic solution can be obtained. We have shown that at the bottom of this miracle is the fact that these systems have the unexpected feature that a non-local tranformation maps the driven version back into an equilibrium one.
The domain of applicability of such a transformation is at present an open question.
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