Dynamics of Dilute Gases at Equilibrium: From the Atomistic Description to Fluctuating Hydrodynamics

Bodineau, Thierry; Gallagher, Isabelle; Saint‐Raymond, Laure; Simonella, Sergio

doi:10.1007/s00023-022-01257-y

Cited by 3 publications

(2 citation statements)

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“…For further discussions on the fluctuation theory of the hard sphere gas we refer to these references, as well as to [12, 27, 28]. By combining cumulant techniques and the weak convergence method of the present paper, we can actually derive the fluctuating Boltzmann equation at equilibrium for long times (see the companion paper [4]).…”

Section: Introductionmentioning

confidence: 99%

“…The weak convergence method discussed in this paper allows actually to construct the limit of higher order moments of the fluctuation field and show their asymptotic factorization according to the Wick rule, providing a central limit theorem and thereby completing the program. This result, which requires a nontrivial combination with the cumulant techniques developed in [5, 6], will be presented in a companion work [4].…”

Section: Introductionmentioning

confidence: 99%

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Long‐time correlations for a hard‐sphere gas at equilibrium

Bodineau

Gallagher

Saint‐Raymond

et al. 2023

Comm Pure Appl Math

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It has been known since Lanford that the dynamics of a hard‐sphere gas is described in the low density limit by the Boltzmann equation, at least for short times. The classical strategy of proof fails for longer times, even close to equilibrium. In this paper, we introduce a weak convergence method coupled with a sampling argument to prove that the covariance of the fluctuation field around equilibrium is governed by the linearized Boltzmann equation globally in time (including in diffusive regimes). This method is much more robust and simpler than the one devised in Bodineau et al which was specific to the 2D case.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Long‐time correlations for a hard‐sphere gas at equilibrium

Bodineau

Gallagher

Saint‐Raymond

et al. 2023

Comm Pure Appl Math

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Long-Time Dynamics in Quantum Spin Lattices: Ergodicity and Hydrodynamic Projections at All Frequencies and Wavelengths

Ampelogiannis

Doyon

2023

Ann. Henri Poincaré

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Obtaining rigorous and general results about the non-equilibrium dynamics of extended many-body systems is a difficult task. In quantum lattice models with short-range interactions, the Lieb–Robinson bound tells us that the spatial extent of operators grows at most linearly in time. But what happens within this light-cone? We discuss rigorous results on ergodicity and the emergence of the Euler hydrodynamic scale in correlation functions, which establish fundamental principles at the root of non-equilibrium physics. One key idea of the present work is that general structures of Euler hydrodynamics, obtained under ballistic scaling, follow independently from the details of the microscopic dynamics, and in particular do not necessitate chaos; they are consequences of “extensivity”. Another crucial observation is that these apply at arbitrary frequencies and wavelengths. That is, long-time, persistent oscillations of correlation functions over ballistic regions of spacetime, which may be of microscopic frequencies and wavelengths, are predicted by a general Euler-hydrodynamic theory that takes the same form as that for smoothed-out correlation functions. This involves a natural extension of notions of conserved quantities and hydrodynamic projection and shows that the Euler hydrodynamic paradigm covers the full frequency-wavelength plane.

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