Title: Proof of Time's Arrow with Perfectly Chaotic Superdiffusion,
Abstract: The problem of Time's Arrow is rigorously solved in a certain microscopic
system associated with a Hamiltonian using only information about the
microscopic system. This microscopic system obeys an equation with time
reversal symmetry. In detail, we prove that a symplectic map with time reversal
symmetry is an Anosov diffeomorphism. This result guarantees that any initial
density function defined except for a zero volume set converges to the unique
invariant density (uniform distribution) in the sense of mixing. In addition,
we discover that there is a mathematical structure which connects Time's Arrow
(Anosov diffeomorphism) with superdiffusion in our system. In particular, the
mechanism of this superdiffusion in our system is different from those
previously found.