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Hydrodynamical limit for a Hamiltonian system with weak noise. (English) Zbl 0781.60101

Summary: Starting from a general Hamiltonian system with superstable pairwise potential, we construct a stochastic dynamics by adding a noise term which exchanges the momenta of nearby particles. We prove that, in the scaling limit, the time conserved quantities, energy, momenta and density, satisfy the Euler equation of conservation laws up to a fixed time \(t\) provided that the Euler equation has a smooth solution with a given initial data up to time \(t\). The strength of the noise term is chosen to be very small (but nonvanishing) so that it disappears in the scaling limit.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B30 Statistical thermodynamics
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