  This paper has been withdrawn by the author. For the reason, see the bottom
paragraph of this abstract.
  By generalizing Tasaki's work on the second law of thermodynamics for an
adiabatic process between two equilibrium states of a macroscopic quantum
compound system, we obtain an extension of the second law to a transient
adiabatic process that takes a macroscopic quantum compound system consisting
of a system of interest and two heat reservoirs from an initial equilibrium
state to a final non-equilibrium state, where the system of interest is in a
steady heat conduction state. For the system of interest, we define its
generalized entropy so that it becomes an experimentally measurable quantity
and exactly satisfies an extension of the Clausius relation.
  This paper has been withdrawn by the author because the generalized entropy
presented in this article violates the second law when the system in a steady
heat conduction state is detached from the two reservoirs and then attached to
a reservoir at the temperature T^bar defined in Sec.1.2 so that it will reach
an equilibrium state at T^bar. In this irreversible process, the total entropy
for the system and the reservoir remains constant and thus violates the second
law.
