In this paper, exact continuum equations are derived to the classical many-body system in the hydrodynamic limit without the utilisation of statistical mechanics. It is shown that the resulting equations are universal for a class of pair potentials, and, unlike in statistical mechanics based coarse-grained models, the momentum density field carries the temperature. Evidence for the presence of pseudo time-irreversible equilibration, heat and momentum transport is provided by analysing numerical solutions of the dynamical equations. The numerical solutions further indicate the presence of non-diffusional relaxation of the macroscopic order, which raises questions about the completeness of the classical many-body dynamics in regards of the second law of thermodynamics.
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