A nonequilibrium statistical ensemble formalism MaxEnt-NESOM: Basic concepts, construction, application, open questions and criticisms

We describe a particular approach for the construction of a nonequilibrium statistical ensemble formalism for the treatment of dissipative many-body s ystems. This is the so-called Nonequilibrium Statistical Operator Method, b ased on the seminal and fundamental ideas set forward by Boltzmann and Gibb s. The existing approaches can be unified under a unique variational princi ple, namely, MaxEnt, which we consider here. The main six basic steps that are at the foundations of the formalism are presented and the fundamental c oncepts are discussed. The associated nonlinear quantum kinetic theory and the accompanying Statistical Thermodynamics (the Informational Statistical Thermodynamics) are very briefly described. The corresponding response func tion theory for systems away from equilibrium allows to connected the theor y with experiments, and some examples are summarized; there follows a good agreement between theory and experimental data in the cases in which the la tter are presently available. We also present an overview of some conceptua l questions and associated criticisms.