  By taking the need for quantum reference frames into account, it is shown
that Hilbert-space factorization is a dissipative process requiring on the
order of kT to reduce by one bit an observer's uncertainty in the provenance of
a classically-recorded observational outcome. This cost is neglected in
standard treatments of decoherence that assume that observational outcomes are
obtained by interacting with a collection of degrees of freedom identified a
priori. Treating this cost explicitly leads to a natural measure of the
probability of any particular quantum reference frame.
