  The Bochkov-Kuzovlev nonlinear fluctuation-dissipation theorem is used to
derive Narayanaswamy's phenomenological theory of physical aging, in which this
highly nonlinear phenomenon is described by a linear material-time convolution
integral. A characteristic property of the Narayanaswamy aging description is
material-time translational invariance, which is here taken as the basic
assumption of the derivation. It is shown that only one possible definition of
the material time obeys this invariance, namely the square of the distance
travelled from a configuration of the system far back in time. The paper
concludes with suggestions for computer simulations that test for consequences
of material-time translational invariance. One of these is the
"unique-triangles property" according to which any three points on the system's
path form a triangle such that two side lengths determine the third; this is
equivalent to the well-known triangular relation for time-autocorrelation
functions of aging spin glasses [L. F. Cugliandolo and J. Kurchan, J. Phys. A:
Math. Gen. 27, 5749 (1994)]. The unique-triangles property implies a simple
geometric interpretation of out-of-equilibrium time-autocorrelation functions,
which extends to aging a previously proposed framework for such functions in
equilibrium [J. C. Dyre, cond-mat/9712222].
