Séminaire du LPTMS: Antonio Prados


11:00 - 12:00

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405
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A general class of dissipative models: fluctuating hydrodynamics and large deviations

A. Prados, Universidad de Sevilla

We consider a general class of models, described at the mesoscopic level by a fluctuating balance equation for the local energy density. This balance equation has a diff usive term, with a current that fluctuates around its average behaviour given by Fourier’s law, and a dissipation term which is a general function of the local energy density. The latter does not include a fluctuating term, as the dissipation fluctuations are enslaved to those of the density due to the (assumed) quasi-elasticity of the underlying microscopic dynamics. This quasi-elasticity of the microscopic dynamics is compatible with the existence of a finite dissipation over the di ffusive time scale which is relevant at the mesoscopic level.
This general fluctuating hydrodynamic picture [1], together with an « additivity conjecture » [2], makes it possible to write the functional giving the probability of large deviations of the dissipated energy from the average behaviour. The functional has the same form as in the non-dissipative case, due to the subdominant role played by the dissipation noise. The above hydrodynamic description is shown to emerge from a general class of models, with stochastic dissipative dynamics at the microscopic level, in the large system size limit. Both the average macroscopic behaviour and the noise properties of the hydrodynamic fields are obtained from the microscopic dynamics. Finally, this general scheme is applied to the simplest dissipative version of the so-called KMP model [3] for heat transport. The theoretical predictions are compared to extensive numerical simulations, and an excellent agreement is found [4-6].

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3. C. Kipnis, C. Marchioro and E. Presutti, J. Stat. Phys. 27, 65 (1982).
4. A. Prados, A. Lasanta and P. I. Hurtado, Phys. Rev. Lett. 107, 140601 (2011).
5. A. Prados, A. Lasanta and P. I. Hurtado, Phys. Rev. E 86, 031134 (2012).
6. P. I. Hurtado, A. Lasanta, and A. Prados, Phys. Rev. E 88, 022110 (2013).

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