  In this paper, the emergence of macroscopic-scale pseudo time-irreversibility
is studied in the closed classical many-body system of pair interacting
particles. First, exact continuum equations are derived to the Hamiltonian
dynamics without the utilisation of statistical mechanics. Next, it is shown
that the momentum density field incorporates the thermal degrees of freedom in
the considered scaling limit, and therefore initial condition indicated pseudo
time-irreversible solutions may exist to the dynamical equations. Numerical
evidence for pseudo-irreversible thermal equilibration, heat and momentum
transport is provided. Finally, the possible reasons of the numerically
obtained non-diffusional relaxation of macroscopic order is discussed.
