Nonequilibrium statistical mechanics, transport equations, and the second law of thermodynamics

A first-principle statistical theory of nonequilibrium processes is attempted based on the assumption of quasiclassical particle motions. This assumption leads to the BBGKY hierarchy which, in addition to physically reasonable solutions, contains solutions contradicting the causality principle. In order to eliminate them, all the distribution functions involved must be expanded as series in the small parameter ε=σ/L, where σ is the particle diameter and L is a characteristic macroscopic length. To zeroth order in ε, the BBGKY hierarchy yields the Gibbs distribution, the first law of thermodynamics, and the equations of the theory of liquids, thus enabling the thermodynamical parameters of a substance to be calculated. To the first order, one obtains (a) a system of five transport equations for five hydrodynamic variables (mass, three velocity components, and temperature), (b) a set of equations for the first-principles calculation of transport coefficients, and (c) the second law of thermodynamics. The possibility of an entropy increase without Liouville's theorem being violated is demonstrated.