A thermodynamics for a system under shear

A thermodynamics is introduced for fluids subjected to a constant shear. The theory is based primarily on the results of computer simulations using the technique of homogeneous shear nonequilibrium molecular dynamics applied to a system of 108 Lennard-Jones particles. It is supported qualitatively by the results of several authors for other systems. The shear rate γ enters explicitly into the description of the fluid: the equation of state is p = p(V,T,γ) and thermodynamic equation is dE = TdS −pdV+ζdγ, where ζ is a state function. Using the relations found previously to be valid for a wide range of γ: p = p0+p1γ3/2 and E = E0+E1γ3/2, the thermodynamics can be checked numerically for consistency and several consequences, such as stability criteria criteria, can be verified. The criteria indicate that phase changes are influenced by the shear rate when the system is subjected to the shear.