General formalism of non-equilibrium statistical mechanics, a path approach

Details General formalism of non-equilibrium statistical mechanics, a path approach General formalism of non-equilibrium statistical mechanics, a path approach

2009-05-31

arxiv.org/abs/0906.0190v4

Physics

Condensed Matter

Statistical Mechanics

Major revision

Scientific paper

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.

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