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We describe the large applicability of the Nonequilibrium Statistical Operator Method (NSOM) for the study of dissipative dynamic systems far from equilibrium. It is shown that the NSOM can be encompassed by a unifying variational principle, which produces a large family of NSO that contains existing examples as particular cases. Further, we review the application of the NSOM for the construction of a nonlinear quantum theory of large scope, and for the generation of a response function theory, for far‐from‐equilibrium Hamiltonian systems. An accompanying non‐equilibrium thermodynamic Green's function theory is briefly described. Also it is shown that the NSOM provides mechano‐statistical foundations for phenomenological irreversible thermodynamics, and for the important question of stability of far‐from‐equilibrium steady states and the emergence of self‐organized dissipative structures in condensed matter.

We briefly, and partially, consider aspects of the present status of phenomenological irreversible thermodynamics and nonequilibrium statistical mechanics. After short comments on Classical Irreversible Thermodynamics, its conceptual and practical shortcomings are pointed out, as well as the efforts undertaken to go beyond its limits, consisting of particular approaches to a more general theory of Irreversible Thermodynamics. In particular, a search for statistical-mechanical foundations of Irreversible Thermodynamics, namely, the construction of a statistical thermodynamics, are based on the Nonequilibrium Statistical Operator Method. This important theory for the treatment of phenomena at the macroscopic level, is based on a microscopic molecular description in the context of a nonequilibrium ensemble formalism. We draw attention to the fact that this method may be considered to be emcompassed within Jaynes' Predictive Statistical Mechanics and based on the principle of maximization of informational entropy. Finally, we describe how, in fact, the statistical method provides foundations to phenomenological irreversible thermodynamics, thus giving rise to what can be referred to as Informational Statistical Thermodynamics.

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We consider the nonequilibrium and dissipative evolution, and the steady state of the population of vibrational polar modes in a chain of biomolecules. These polar modes are excited through a coupling with a metabolic pumping source and are in anharmonic interaction with an elastic continuum. Groups of polar modes are coupled in this way through nonlinear terms in the kinetic equations. This nonlinearity is shown to be the source of an unexpected phenomenon characterizing complex behavior in this kind of system: after a threshold of intensity of the pumping source is achieved, polar modes with the lowest frequencies increase enormously their population in a way reminiscent of a Bose-Einstein condensation (Frohlich effect)~The transient time for the steady-state condensate to follow is very short (picosecond time scale) and the condensation appears even for weak values of the anharmonic coupling strength responsible for its occurrence. Further, it seemingly requires accessible levels of metabolic pumping power in order to be produced and sustained.PACS number(s): 87.10.+e, 05.70.Ln