Abstract
We investigate the time evolution of a model system of interacting particles moving in a d-dimensional torus. The microscopic dynamics is first order in time with velocities set equal to the negative gradient of a potential energy term Ψ plus independent Brownian motions: Ψ is the sum of pair potentials, V(r)+γ d J(γr); the second term has the form of a Kac potential with inverse range γ. Using diffusive hydrodynamic scaling (spatial scale γ −1, temporal scale γ −2) we obtain, in the limit γ↓0, a diffusive-type integrodifferential equation describing the time evolution of the macroscopic density profile.
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Buttà, P., Lebowitz, J.L. Hydrodynamic Limit of Brownian Particles Interacting with Short- and Long-Range Forces. Journal of Statistical Physics 94, 653–694 (1999). https://doi.org/10.1023/A:1004512807858
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DOI: https://doi.org/10.1023/A:1004512807858