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Non equilibrium steady states: fluctuations and large deviations of the density and of the current

B. Derrida
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Abstract

These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow to calculate the fluctuations and large deviations of the density and of the current in non-equilibrium steady states of systems like exclusion processes. The properties of these fluctuations and large deviation functions in non-equilibrium steady states (for example non-Gaussian fluctuations of density or non-convexity of the large deviation function which generalizes the notion of free energy) are compared with those of systems at equilibrium.

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B. Derrida. 2007-03-28. Non equilibrium steady states: fluctuations and large deviations of the density and of the current. https://doi.org/10.1088/1742-5468%2F2007%2F07%2Fp07023

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