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We derive the system of equations that allows to include non-equilibriumcorrelations of filling numbers into the theory of the hopping transport. Thesystem includes the correlations of arbitrary order in a universal way and canbe cut at any place relevant to a specific problem to achieve the balancebetween rigor and computation possibilities. In the linear-responseapproximation, it can be represented as an equivalent electric circuit thatgeneralizes the Miller-Abrahams resistor network. With our approach, we showthat non-equilibrium correlations are essential to calculate conductivity anddistribution of currents in certain disordered systems. Different types ofdisorder affect the correlations in different applied fields. The effect ofenergy disorder is most important at weak electric fields while the positiondisorder by itself leads to non-zero correlations only in strong fields.

The system of correlation kinetic equations and the generalized equivalent circuit for hopping transport