A CLASSICAL APPROACH IN PREDICTIVE STATISTICAL-MECHANICS - A GENERALIZED BOLTZMANN FORMALISM

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.