  We apply linear response theory to a general, inhomogeneous, stationary
stellar system, with particular emphasis on dissipative processes analogous to
Landau damping. Assuming only that the response is causal, we show that the
irreversible work done by an external perturber is described by the
anti-Hermitian part of a linear response operator, and damping of collective
modes is described by the anti-Hermitian part of a related polarization
operator. We derive an exact formal expression for the response operator, which
is the classical analog of a well-known result in quantum statistical physics.
When the self-gravity of the response can be ignored, and the ensemble-averaged
gravitational potential is integrable, the expressions for the mode energy,
damping rate, and polarization operator reduce to well-known formulae derived
from perturbation theory in action-angle variables. In this approximation,
dissipation occurs only via resonant interaction with stellar orbits or
collective modes. For stellar systems in thermal equilibrium, the
anti-Hermitian part of the response operator is directly related to the
correlation function of the fluctuations. Thus dissipative properties of the
system are completely determined by the spectrum of density fluctuations---the
fluctuation-dissipation theorem. In particular, we express the coefficient of
dynamical friction for an orbiting test particle in terms of the fluctuation
spectrum; this reduces to the known Chandrasekhar formula in the restrictive
case of an infinite homogeneous system with a Maxwellian velocity distribution.
