Summary
We investigate the ergodic properties of Hamiltonian systems subjected to local random, energy conserving perturbations. We prove for some cases, e.g. anharmonic crystals with random nearest neighbor exchanges (or independent random reflections) of velocities, that all translation invariant stationary states with finite entropy per unit volume are microcanonical Gibbs states. The results can be utilized in proving hydrodynamic behavior of such systems.
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Hill Center for Mathematical Sciences, Rutgers University, New Brunswick, NJ 08903, USA
JF was supported in parts by Japan Society for Promotion of Science (JSPS) and by NSF Grant DMR89-18903
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Fritz, J., Funaki, T. & Lebowitz, J.L. Stationary states of random Hamiltonian systems. Probab. Th. Rel. Fields 99, 211–236 (1994). https://doi.org/10.1007/BF01199023
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DOI: https://doi.org/10.1007/BF01199023