From Reversible Many-Body Dynamics to Newtonian Viscosity-An Infinite Mori-Hierarchy Viscosity Operator and Testable Predictions-

This paper proposes a theoretical framework in which the Newtonian viscosity coefficient is interpreted not as a fundamental instantaneous constant, but as the low-frequency and long-wavelength limit of a frequency-dependent transport operator generated by an infinite Mori hierarchy. Starting from the local conservation law of momentum, the paper argues that the first Mori coefficient associated with the transverse momentum mode should be proportional to the square of the wave number in the hydrodynamic limit. The higher Mori coefficients are interpreted as representing progressively more microscopic time scales. Using the Mori recurrence hierarchy, the transverse memory kernel is expressed as an infinite continued fraction. This structure is then interpreted as a frequency-dependent viscosity operator containing the full hierarchy of microscopic relaxation processes. Within this framework, ordinary Newtonian viscosity is recovered as the low-frequency limit of the memory operator, while the standard Navier–Stokes equation appears as the short-memory, or Markovian, limit of a more general time-nonlocal hydrodynamic equation. The purpose of this paper is not to introduce memory functions, generalized hydrodynamics, or the Mori continued-fraction representation as new concepts. Rather, it reorganizes these established ideas into a concrete and testable hierarchical picture connecting reversible many-body dynamics, the infinite Mori chain, frequency-dependent viscosity, and the Navier–Stokes limit. Two preliminary molecular-dynamics checks are included in the appendices. The first indicates that the first Mori coefficient divided by the square of the wave number approaches a finite value as the wave number decreases, consistent with the predicted hydrodynamic scaling. The second indicates that the next Mori coefficient remains finite and approximately independent of the hydrodynamic wave number. These calculations are intended only as preliminary consistency checks. Systematic numerical validation of higher Mori levels, finite-size effects, the low-frequency limit, and the emergence of the full Navier–Stokes viscosity will be addressed in subsequent work.