  The quantum master equation obtained by generalizing the geometric
formulation of nonequilibrium thermodynamics to dissipative quantum systems is
seriously nonlinear. We argue that nonlinearity occurs naturally in the step
from reversible to irreversible equations and we analyze the nature of the
nonlinear contribution. The thermodynamic nonlinearity leads to proper
equilibrium solutions and improves the dynamic behavior of dissipative quantum
systems. We also discuss the Markovian character of the thermodynamic quantum
master equation. The general ideas are illustrated for two-level systems.
