The transport properties of soft particle glasses, such as dynamic viscosity, normal stress coefficients, and shear-induced diffusivity of its particles, are determined by the microstructure of the suspension under flow. A thermodynamic measure of the microstructure is the excess entropy, which we show here accurately correlates the transport properties of soft particle glasses onto master curves across a wide range of volume fractions, suspending fluid viscosities, particle moduli, and shear rates. The excess entropy for soft particle glasses is approximated with the two-body excess entropy computed from the pair distribution function extracted from dynamic simulations. The shear viscosity and normal stress functions diverge and the diffusivity vanishes at a critical excess entropy, corresponding to the yield stress of the suspension. An effective temperature is computed and is found to vary linearly with the shear stress and the elastic energy of the sheared soft particle glass. From this, an equation of state is derived relating the excess entropy to the shear stress. Consequently, three of the four transport properties are determined from the measurement of just one. Finally, a single master curve of particle diffusivity versus excess entropy is presented that unifies observations for both equilibrium and nonequilibrium suspensions.