  We compare the thermodynamic entropy of a quantum Brownian oscillator derived
from the partition function of the subsystem with the von Neumann entropy of
its reduced density matrix. At low temperatures we find deviations between
these two entropies which are due to the fact that the Brownian particle and
its environment are entangled. We give an explanation for these findings and
point out that these deviations become important in cases where statements
about the information capacity of the subsystem are associated with
thermodynamic properties, as it is the case for the Landauer principle.
