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We study a minimal non-Markovian model of superdiffusion which originates from long-range velocity correlations within the generalized Langevin equation approach. The model allows for a three-dimensional Markovian embedding. The emergence of a transient hyperdiffusion, ⟨x^2 (t) ⟩t^2+, with 1--3 is detected in tilted washboard potentials before it ends up in a ballistic asymptotic regime. We relate this phenomenon to a transient heating of particles T₊₈₍ (t) t^ from the thermal bath temperature T to some maximal kinetic temperature T₌₀ₗ. This hyperdiffusive transient regime ceases when the particles arrive at the maximal kinetic temperature.
Siegle et al. (Wed,) studied this question.
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