Ensemble formalism for nonequilibrium systems and an associated irreversible statical thermodynamics

Abstract

It is reviewed what can be considered as the present research trends in what regards to the construction of an ensemble formalism -Gibbs' style -for the case of far-from-equilibrium systems. The main questions involved are presented accompanied with brief discussions. The construction of a nonequilibrium statistical operator is described and its applications commented, and, particularly, it is presented the derivation of an Irreversible Thermodynamics based on the statistical foundations that the nonequilibrium ensemble formalism provides.

Nonequilibrium temperature and thermometry in heat-conductingϕ4models

“…is imposed. Symmetry suggests that the temperature difference should depend quadratically on the heat flux (this same dependence is also predicted by "extended irreversible thermodynamics" [8,9,10,11,17,20,24]). These simple arguments are wrong.…”

“…In discussing the applicability of irreversible thermodynamics to nonequilibrium systems several workers have suggested the use of a "local thermodynamic equilibrium" temperature [5,8,11,17,20,24]. For the present model the relation between the local thermodynamic equilibrium temperature and the kinetic temperature is nearly linear.…”

“…For a comprehensive review of efforts based on a nonequilibrium Gibbs entropy, presumably −k ln f noneq , see Ref. [20]. It is evident that such efforts are inconsistent with what is known about the singular fractal nature of nonequilibrium phase space distributions, { f noneq }.…”

Josef Meixner: His life and his orthogonal polynomials

“…Shortly thereafter, Mazur and de Groot joined this group as founding fathers of the new field of nonequilibrium thermodynamics". Furthermore, A. R. Vasconcellos et al [80] write: "J. Meixner, over twenty years ago in papers that did not obtain a deserved diffusion gave some convincing arguments to show that it is unlikely that a nonequilibrium . .…”