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

## TL;DR

This paper develops a comprehensive system of equations to incorporate non-equilibrium correlations into hopping transport theory, enabling more accurate modeling of conductivity in disordered systems and generalizing the Miller-Abrahams resistor network.

## Contribution

It introduces a universal system of correlation equations that can be truncated for specific problems and represents them as an equivalent circuit in linear response.

## Key findings

- Non-equilibrium correlations are crucial for accurate conductivity calculations.
- Energy disorder dominates at weak fields, while position disorder influences strong fields.
- The approach generalizes the resistor network model for disordered systems.

## Abstract

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