  A systematic expansion of the many-body master equation for active matter, in
which motors power configurational changes as in the cytoskeleton, is shown to
yield a description of the steady state and responses in terms of an effective
temperature. The effective temperature depends on the susceptibility of the
motors and a Peclet number which measures their strength relative to thermal
Brownian diffusion. The analytic prediction is shown to agree with previous
numerical simulations and experiments. The mapping also establishes a
description of aging in active matter that is also kinetically jammed.
