  Use of the extended definition of heat dQ=deQ+diQ converts the Clausius
inequality dS greater than or equal to deQ/T0 into an equality dS=dQ/T
involving the nonequilibrium temperature T of the system having the
conventional interpretation that heat flows from hot to cold. The equality is
applied to the exact quantum evolution of a 1-dimensional ideal gas free
expansion. In a first ever calculation of its kind in an expansion which
retains the memory of initial state, we determine the nonequilibrium
temperature T and pressure P, which are then compared with the ratio P/T
obtained by an independent method to show the consistency of the nonequilibrium
formulation. We find that the quantum evolution by itself cannot eliminate the
memory effect.cannot eliminate the memory effect; hence, it cannot thermalize
the system.
