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Nonequilibrium shear viscosity computations with Langevin dynamics. (English) Zbl 1246.82092

Multiscale Model. Simul. 10, No. 1, 191-216 (2012); erratum ibid. 11, No. 1, 410-410 (2013).
Summary: We study the mathematical properties of a nonequilibrium Langevin dynamics which can be used to estimate the shear viscosity of a system. More precisely, we prove a linear response result which allows us to relate averages over the nonequilibrium stationary state of the system to equilibrium canonical expectations. We then write a local conservation law for the average longitudinal velocity of the fluid and show how, under some closure approximation, the viscosity can be extracted from this profile. We finally characterize the asymptotic behavior of the velocity profile, in the limit where either the transverse or the longitudinal friction goes to infinity. Some numerical illustrations of the theoretical results are also presented.
In the erratum we present required modifications in the proofs of Theorems 2 and 3.

MSC:

82C70 Transport processes in time-dependent statistical mechanics
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
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