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The theory of nonlinear transport is elaborated to determine the Burnett transport properties of non-ideal multi-element plasma and neutral systems. The procedure for the comparison of the phenomenological conservation equations of a continuous dense medium and the microscopic equations for dynamical variable operators is used for the definition of these properties. The Mori algorithm is developed to derive the equations of motion of dynamical value operators of a non-ideal system in the form of the generalized nonlinear Langevin equations. In consequence, the microscopic expressions of transport coefficients corresponding to second-order thermal disturbances (temperature, mass velocity, etc) have been found in the long wavelength and low frequency limits.

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Key words Strongly-coupled plasmas, nonlinearity and bifurcation, heat and mass transfer in the Burnett approximation.The theory of non-linear transport is elaborated to determine the Burnett transport properties of non-ideal multielement plasma and neutral systems. The procedure of the comparison of the phenomenological conservation equations of a continuous dense medium and the microscopic equations for dynamical variables operators in the form of the generalized nonlinear Langevin equations is used for the definition of these properties. In consequence, the microscopic expressions of transport coefficients corresponding to second order thermal disturbances (temperature, mass velocity, etc.) have been found in the long-wavelength and low frequency limits of correlations functions. Situations are considered when the use of nonlinear transport characteristics (in the Burnett approximation) significantly affects the results of modeling of hydrodynamic processes in dense charged and neutral media.