  We develop a free energy framework to describe the response of glasses to
applied stress. Unlike crystals, for which the free energy increases
quadratically with strain due to affine displacements, for glasses, the
nonequilibrium free energy decreases due to complex interplay of non-affine
displacements and dissipation. We measure this free energy directly in strained
colloidal glasses, and use mean-field theory to relate it to affine and
nonaffine displacements. Nonaffine displacements grow with applied shear due to
shear-induced loss of structural connectivity. Our mean-field model allows for
the first time to disentangle the complex contributions of affine and nonaffine
displacements and dissipation in the transient deformation of glasses.
