Ujjwal,
Indeed, they don't have the same status:
• Thermally activated hopping conduction is a physical phenomenon. The one-electron wave function is hopping from one site to a neighbor one, each time overcoming an energy barrier that is at first order equal to the observed activation energy, although there might be some corrections due among others to entropy factor or lattice relaxation. The prefactor is related to the eigenfrequency of the ground state.
• The Meyer-Neldel rule (1937) is an empirical law describing a correlation between prefactor and activation energy in transport experiments in disordered materials. None of the theoretical models proposed to explain the origin of the Meyer-Neldel rule is universally accepted. It seems that several effects, depending on the materials and conditions, may lead to a similar global behavior. Many authors stress out that prefactors for the conductivity provided by the Meyer-Neldel interpretation are difficult to interpret physically. Look e.g. at Widenhorn et al., JAP 89, 8179 (2001), Widenhorn et al., JAP 91, 6524 (2002).
In that sense, the status of the Meyer-Neldel rule is similar to that of 1/f noise. Both are a commonly encountered behavior in many types of materials and devices, but they don't convey much physical information.
There is now some agreement that 1/f noise originates from the incoherent superposition of many discrete lorentzian fluctuators, with time constants ranging from values shorter than the time constant of the experimental equipment to values longer than the duration of the experiment. In a certain sense, this is smearing brought to its limit. For an enlightening insight of 1/f noise in semiconductor devices, see Kirton and Uren, Advances in Physics 38, 367-468, 1989.
Hopefully this can help you.
Best regards,
Vincent Mosser
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