  A model computational quantum thermodynamic network is constructed with two
variable temperature baths coupled by a linker system, with an asymmetry in the
coupling of the linker to the two baths. It is found in computational
simulations that the baths come to "thermal equilibrium" at different bath
energies and temperatures. In a sense, heat is observed to flow from cold to
hot. A description is given in which a recently defined quantum entropy
$S^Q_{univ}$ for a pure state "universe" continues to increase after passing
through the classical equilibrium point of equal temperatures, reaching a
maximum at the asymmetric equilibrium. Thus, a second law account $\Delta
S^Q_{univ} \ge 0$ holds for the asymmetric quantum process. In contrast, a von
Neumann entropy description fails to uphold the entropy law, with a maximum
near when the two temperatures are equal, then a decrease $\Delta S^{vN} < 0$
on the way to the asymmetric equilibrium.
