A Classical Approach in Predictive Statistical Mechanics: A Generalized Boltzmann Formalism

We consider a mechano‐statistical formalism for the description of nonequilibrium classical Hamiltonian many‐body systems. It is described how such formalism, the so called nonequilibrium statistical operator method 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 is shown how to obtain a nonlinear generalized transport theory of large scope. This theory is applied to derive the equations of evolution for the single‐ and two‐particle distribution functions to obtain generalized transport equations including relaxation effects to all orders in the interaction strength, valid, in principle, for arbitrary nonequilibrium dissipative states. The classical Boltzmann equation and Boltzmann's H ‐theorem are recovered within restrictive approximations. Finally we discuss the connection with phenomenological irreversible thermodynamics, for which the method provides microscopic foundations in what is termed Informational Statistical Thermodynamics. The questions of entropy production and a generalized H ‐theorem are considered and conceptual aspects of the method are discussed.