  The concept of weak invariants is examined in the thermodynamic context.
Discussions are made about the temporally-local equilibrium states, corrections
to them, and isoenergetic processes based on the quantum master equations of
the Lindblad type that admit time-dependent Hamiltonians as weak invariants.
The method for determining the correction presented here may be thought of as a
quantum-mechanical analog of the Chapman-Enskog expansion in nonequilibrium
classical statistical mechanics. Then, the theory is applied to the
time-dependent harmonic oscillator as a simple example, and the power output
and the work along an isoenergetic process are evaluated within the framework
of finite-time quantum thermodynamics.
