Nonlinear irreversible fluxes in a fluid with large shear rate

Generalized Green‐Kubo expressions are used to describe the nonlinear dependence of the irreversible heat and momentum fluxes on the thermodynamic forces for a simple fluid. Formally exact equations for these fluxes are evaluated for conditions of large shear flow. The associated non‐equilibrium time correlation functions are evaluated exactly to linear order in the temperature and pressure gradients, and to arbitrary order in the shear rate, for a low‐density gas of Maxwell molecules. Modifications of Fourier's heat law and Newton's viscosity law are obtained in terms of transport coefficients that depend on the shear rate. This dependence on shear rate is illustrated for several of the transport coefficients.