Jg. Ramos et al., A CLASSICAL APPROACH IN PREDICTIVE STATISTICAL-MECHANICS - A GENERALIZED BOLTZMANN FORMALISM, Fortschritte der Physik, 43(4), 1995, pp. 265-300
We consider a mechano-statistical formalism for the description of non
equilibrium classical Hamiltonian many-body systems. It is described h
ow such formalism, the so called nonequilibrium statistical operator m
ethod at the classical mechanical level is obtained through the use of
a variational principle that recovers known approaches as particular
cases. The method is shown to be encompassed in the context of Jaynes'
Predictive Statistical Mechanics. On the basis of this formalism it i
s shown how to obtain a nonlinear generalized transport theory of larg
e scope. This theory is applied to derive the equations of evolution f
or the single- and two-particle distribution functions to obtain gener
alized transport equations including relaxation effects to all orders
in the interaction strength, valid, in principle, for arbitrary nonequ
ilibrium dissipative states. The classical Boltzmann equation and Bolt
zmann's H-theorem are recovered within restrictive approximations. Fin
ally we discuss the connection with phenomenological irreversible ther
modynamics, for which the method provides microscopic foundations in w
hat is termed Informational Statistical Thermodynamics. The questions
of entropy production and a generalized H-theorem are considered and c
onceptual aspects of the method are discussed.