  The virial theorem is established in the framework of resolution-scale
relativity for stochastic dynamics characterized by a diffusion constant D. It
only relies on a simple time average just like the classical virial theorem,
while the quantum mechanical virial theorem involves the expectation values of
the observables. Nevertheless, by the emergence of a quantum-like potential
term, the resolution-scale relativity virial theorem also encompasses quantum
mechanical dynamics under the identification hbar <--> 2mD. This provides an
illustration of the scale relativistic approach to the foundation of standard
quantum mechanics. Furthermore, it is pointed out that, if the resolution-scale
relativity principle is implemented in macroscopic systems that are complex
and/or chaotic, then the application of the classical virial theorem in the
analysis of the dynamics of astrophysical systems neglects the contribution
from a resolution-scale relativistic quantum-like potential. It is shown that
this quantum-like potential could account for some fraction of the dark matter
hypothesis.
