Nonlinear Effects in Transport Theory

A method for the formal statistical description of transport processes beyond the linear approximation is discussed. External forces which maintain a deviation from equilibrium are introduced into the Liouville equation, and solution of this equation yields an ensemble characteristic of the non-equilibrium state. The transport relations are obtained with the aid of the resulting ensemble. For simplicity, the discussion is restricted to heat flow, but the generalization to the processes of viscosity and diffusion is straightforward.