Mapping out of equilibrium into equilibrium

Jorge Kurchan
École Supérieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI)

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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