  Quantum fluctuations, through quantum corrections, have the potential to lead
to irreversibility in quantum field theory. We consider the virtual ``charge"
distribution generated by quantum corrections in the leading log, short range
approximation, and adopt for it a statistical interpretation. This virtual
charge density has fractal structure, and it is seen that, independently of
whether the theory is or is not asymptotically free, it describes a system
where the equilibrium state is at its classical limit ($\hbar \rightarrow 0$).
We also present a simple analysis of how diffusion of the charge density
proceeds as a function of the distance at which the system is probed.
