  We present a new theoretical formulation of non-equilibrium superconducting
phenomena, including singlet and triplet pairing. We start from the general
Keldysh-Nambu-Gor'kov Green's functions in the quasiclassical approximation and
represent them in terms of 2x2 spin-matrix coherence functions and distribution
functions for particle-type and hole-type excitations. The resulting transport
equations for the distribution functions may be interpreted as a generalization
to the superconducting state of Landau's transport equation for the normal
Fermi liquid of conduction electrons. The equations are well suited for
numerical simulations of dynamical phenomena. Using our formulation we solve an
open problem in quasiclassical theory of superconductivity, the derivation of
an explicit representation of Zaitsev's nonlinear boundary conditions [A.V.
Zaitsev, JETP 59, 1015 (1984)] at surfaces and interfaces. These boundary
conditions include non-equilibrium phenomena and spin singlet and triplet
unconventional pairing. We eliminate spurious solutions as well as numerical
stability problems present in the original formulation. Finally, we formulate
the Andreev scattering problem at interfaces in terms of the introduced
distribution functions and present a theoretical analysis for the study of time
reversal symmetry breaking states in unconventional superconductors via Andreev
spectroscopy experiments at N-S interfaces with finite transmission. We include
impurity scattering self consistently.
