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By Matteo Colangeli

Advent -- From the section area to the Boltzmann Equation -- tools of decreased Description -- Hydrodynamic Spectrum of easy Fluids -- Hydrodynamic Fluctuations from the Boltzmann Equation -- Grad's 13-Moments approach -- Conclusions

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From kinetic models to hydrodynamics : some novel results

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Rondoni and A. Vulpiani, Fluctuation-Dissipation: Response Theory in Statistical Physics, Phys. Rep. 461, 111 (2008). 4. V. Lucarini and M. Colangeli, beyond the linear fluctuation-dissipation theorem: the role of causality, J. Stat. Mech. P05013 (2012). 5. M. Colangeli, L. Rondoni and A. Vulpiani, Fluctuation-dissipation relation for chaotic nonhamiltonian systems, J. Stat. Mech. L04002 (2012). 6. L. D. Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Macroscopic fluctuation theory for stationary non-equilibrium states, J.

2. L. E. Reichl, A modern course in statistical physics (University of Texas Press, Austin, 1980). 3. U. Marini Bettolo Marconi, A. Puglisi, L. Rondoni and A. Vulpiani, Fluctuation-Dissipation: Response Theory in Statistical Physics, Phys. Rep. 461, 111 (2008). 4. V. Lucarini and M. Colangeli, beyond the linear fluctuation-dissipation theorem: the role of causality, J. Stat. Mech. P05013 (2012). 5. M. Colangeli, L. Rondoni and A. Vulpiani, Fluctuation-dissipation relation for chaotic nonhamiltonian systems, J.

Nevertheless, molecular dynamics simulations for argon-like liquids [9] reveal that in the intermediate regime, there are deviations of about 10% from the assumed Gaussian behavior. 2 Linearized Hydrodynamics and Collective Modes 47 between the two asymptotic regimes (represented by the red dashed line in the right panel of Fig. 1). A traditional strategy is based on the introduction of nonlocal hydrodynamic variables and nonlocal transport coefficients, which can be obtained, in a somewhat empirical manner, by solving a generalized Langevin equation [1].

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