  At least one dimensionless physical constant (i.e., a physically observable)
must change for the cosmic time to make the varying speed of light (VSL) models
phenomenologically feasible. Various physical constants and quantities also
should be functions of cosmic time to satisfy all known local laws of physics,
including special relativity, thermodynamics, and electromagnetism. Adiabatic
condition is another necessary condition to keep the homogeneity and isotropy
of three-dimensional space. To be a self-consistent theory, one should consider
cosmic evolutions of physical constants and quantities when one derives
Einstein's field equations and their solutions. All these conditions are well
satisfied in the so-called minimally extended varying speed of light (meVSL)
model. Unlike other VSL models, we show that the redshift-drift formula of the
meVSL model is the same as a standard model. Therefore, we cannot use this as
an experimental tool to verify the meVSL. Instead, one can still use the
cosmological chronometers (CC) as a model-independent test of the meVSL. The
current CC data cannot distinguish meVSL from the standard model (SM) when we
adopt the best-fit values (or Gaussian prior) of the present values of $H_0$
and of $\Omega_{m0}$ from the Planck mission. However, the CC data prefer the
meVSL when we choose Pantheon 22 data.
