The isoentropic, but energy-nonconserving, time evolution of mixed quantum states is
studied in quantum mechanics and quantum field theory. A variational principle, which gives
the Liouville–von Neumann equation, is implemented approximately by making a Gaussian
Ansatz for the density matrix. The dynamical equations governing the parameters that define
the Ansatz satisfy equations variously analogous to the Schrödinger equation and to
mechanical problems. Interesting nonequilibrium evolution is found in special cases, as, for …

A formulation of the non-equilibrium statistical mechanics for quantum fields is given, by
following the equations of motion of finite time intervals. The step length is interpreted in
various models, such as the free and weakly interacting boson field. A detailed calculation
ofthe thermal conductivity is presented in these models and moreover an estimate is given
for the thermal conductivity in quarkless L-QCD using strong coupling methods with the
result: ei/Te, To TK= 10-2 TO=~--