Liouville Ergodicity of Linear Multi-Particle Hamiltonian System with One Marked Particle Velocity Flips

A.A. Lykov, V.A. Malyshev

2015, v.21, №2, 381-412


We consider multi-particle systems with linear deterministic hamiltonian
dynamics. Besides Liouville measure it has continuum of invariant
tori and thus continuum of invariant measures. But
if one specified
particle is subjected to a simple linear deterministic transformation
(velocity flip) in random time moments,
we prove convergence to Liouville
measure for any initial state. For the proof it appeared necessary
to study non-linear transformations on the energy surface.

Keywords: non-equilibrium statistical mechanics, convergence to equilibrium, Liouville measure


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