  The kinetic Glauber-Ising spin chain is one of the very few exactly solvable
models of non-equilibrium statistical mechanics. Nevertheless, existing
solutions do not yield tractable expressions for two-time correlation and
response functions of observables involving products of more than one or two
spins. We use a new approach to solve explicitly the full hierarchy of
differential equations for the correlation and response functions. From this
general solution follow closed expressions for arbitrary multispin two-time
correlation and response functions, for the case where the system is quenched
from equilibrium at T_i > 0 to some arbitrary T >= 0. By way of application, we
give the results for two and four-spin two-time correlation and response
functions. From the standard mapping, these also imply new exact results for
two-time particle correlation and response functions in one-dimensional
diffusion limited annihilation.
