  In this paper we develop a general formalism of a path approach for
non-equilibrium statistical mechanics. Firstly, we consider the classical Gibbs
approach for states and find that this formalism is ineffective for
non-equilibrium phenomena because it is based on a distribution of
probabilities indirectly. Secondly, we develop a path formalism which is
directly based on the distribution of probabilities and therefore significantly
simplifies the analytical approach. The new formalism requires generalizing the
'static', state quantities of a system, like entropy or free energy potential,
to their path analogues. Also we obtain a path balance equation and an equation
of equilibrium path. For the distribution of probabilities we obtain a
functional dependence similar to the Feynman's path integral formalism of
action, only now the role of a Hamiltonian is played by the state entropy. For
the production of the state free energy we illustrate a significant dependence
on the type of system's connectivity.
