  We present a version of soft glassy rheology that includes thermalized strain
degrees of freedom. It fully specifies systems' strain-history-dependent
positions on their energy landscapes and therefore allows for quantitative
analysis of their heterogeneous yielding dynamics and nonequilibrium
deformation thermodynamics. As a demonstration of the method, we illustrate the
very different characteristics of fully-thermal and nearly-athermal plasticity
by comparing results for thermalized and nonthermalized plastic flow.
