  We discuss and motivate the form of the generator of a nonlinear quantum
dynamical group 'designed' so as to accomplish a unification of quantum
mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum
Thermodynamics (QT). Its conceptual foundations differ from those of (von
Neumann) quantum statistical mechanics (QSM) and (Jaynes) quantum information
theory (QIT), but for thermodynamic equilibrium (TE) states it reduces to the
same mathematics, and for zero entropy states it reduces to standard unitary
QM. The nonlinear dynamical group of QT is construed so that the second law
emerges as a theorem of existence and uniqueness of a stable equilibrium state
for each set of mean values of the energy and the number of constituents. It
implements two fundamental ansatzs. The first is that in addition to the
standard QM states described by idempotent density operators (zero entropy), a
strictly isolated system admits also states that must be described by
non-idempotent density operators (nonzero entropy). The second is that for such
additional states the law of causal evolution is determined by the simultaneous
action of a Schroedinger-von Neumann-type Hamiltonian generator and a nonlinear
dissipative generator which conserves the mean values of the energy and the
number of constituents, and (in forward time) drives any density operator, no
matter how far from TE, in the 'direction' of steepest entropy ascent (maximal
entropy increase). The equation of motion can be solved not only in forward
time, to describe relaxation towards TE, but also backwards in time, to
reconstruct the 'ancestral' or primordial lowest entropy state or limit cycle
from which the system originates.
