A deforming solid, containing large numbers of defects, is an intrinsically chaotic system that must on average be moving toward states of increasing probability. In other words, some form of the second law of thermodynamics must be applicable. The relevant thermodynamics, however, must be expressed in terms of an effective disorder temperature, and not just the ordinary kinetic temperature. I will summarize these points, and then show a few examples of how they have been used in shear-transformation-zone (STZ) theories of amorphous plasticity. Time permitting, these examples will include a comparison with experimental data for a metallic glass, an analogous comparison for a numerical simulation of thermalized hard spheres, and an analysis of necking and failure of a stressed thin plate.