  We consider a regular chain of quantum particles with nearest neighbour
interactions in a canonical state with temperature $T$. We analyse the
conditions under which the state factors into a product of canonical density
matrices with respect to groups of $n$ particles each and under which these
groups have the same temperature $T$. In quantum mechanics the minimum group
size $n_{min}$ depends on the temperature $T$, contrary to the classical case.
We apply our analysis to a harmonic chain and find that $n_{min} = const.$ for
temperatures above the Debye temperature and $n_{min} \propto T^{-3}$ below.
