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Thermodynamique des histoires et fluctuations hors d'équilibre

Abstract : Thermodynamics is aimed at studying the fluctuations of configurations in physical systems. This approach is not well fitted to systems where the fluctuations of the histories followed by the system are also important.

In a first part, we translate the Ruelle formalism to the case of
continuous-time Markov systems. The main tools of the theory
(dynamical partition function, topological pressure) appear as large
deviation functions of well-defined time-extensive observables. We
develop a mean-field approach based on a Landau-Ginzburg dynamical free energy construction, from which the main objects of the theory are deduced in a natural way. We also present an algorithm which can be used to evaluate them in finite dimension. In this context, we show that the steady state of glass formers takes place at a first-order coexistence line between active and inactive dynamical phases, which justifies the heuristic picture of dynamical coexistence of phase proposed to describe these models.

The second part deals specifically with current fluctuations in
systems where few general results had been obtained (i) a spin model driven very far from equilibrium; (ii) the symetric exclusion process in dimension one; (iii) examples of superdiffusive systems. In these systems, we determine the power behavior and, when possible, the scaling functions of the current large deviation function, which correspond to different transport regimes in the system.
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https://tel.archives-ouvertes.fr/tel-00198144
Contributor : Vivien Lecomte <>
Submitted on : Sunday, December 16, 2007 - 9:14:26 PM
Last modification on : Wednesday, September 16, 2020 - 4:04:54 PM
Long-term archiving on: : Monday, April 12, 2010 - 8:06:14 AM

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  • HAL Id : tel-00198144, version 1

Citation

Vivien Lecomte. Thermodynamique des histoires et fluctuations hors d'équilibre. Physique mathématique [math-ph]. Université Paris-Diderot - Paris VII, 2007. Français. ⟨tel-00198144⟩

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