  We consider a toy model of pointer interacting with a 1/2-spin system, whose
$\sigma_{x}$ variable is \emph{measured} by the environment, according to the
prescription of decoherence theory. If the environment measuring the variable
$\sigma_{x}$ yields ordinary statistical mechanics, the pointer sensitive to
the 1/2-spin system undergoes the same, exponential, relaxation regardless of
whether real collapses or an entanglement with the environment, mimicking the
effect of real collapses, occur. In the case of non-ordinary statistical
mechanics the occurrence of real collapses make the pointer still relax
exponentially in time, while the equivalent picture in terms of reduced density
matrix generates an inverse power law relaxation.
