Kinetic Field Theory: Cosmic Structure Formation and
  Fluctuation-Dissipation Relations
  Building upon the recently developed formalism of Kinetic Field Theory (KFT)
for cosmic structure formation by Bartelmann et al., we investigate a kinematic
relationship between diffusion and gravitational interactions in cosmic
structure formation. In the first part of this work we explain how the process
of structure formation in KFT can be separated into three processes, particle
diffusion, the accumulation of structure due to initial momentum correlations
and interactions relative to the inertial motion of particles. We study these
processes by examining the time derivative of the non-linear density power
spectrum in the Born approximation. We observe that diffusion and accumulation
are delicately balanced because of the Gaussian form of the initial conditions,
and that the net diffusion, resulting from adding these two counteracting
contributions, approaches the contributions from the interactions in amplitude
over time. This hints at a kinematic relation between diffusion and
interactions in KFT. Indeed, in the second part, we show that the response of
the system to arbitrary gradient forces is directly related to the evolution of
particle diffusion in the form of kinematic fluctuation-dissipation relations
(FDRs). This result is independent of the interaction potential. We show that
this relationship roots in a time-reversal symmetry of the underlying
generating functional. Furthermore, our studies demonstrate how FDRs
originating from purely kinematic arguments can be used in theories far from
equilibrium.
