  Nonthermal relativistic plasmas are ubiquitous in astrophysical systems like
pulsar wind nebulae and active galactic nuclei, as inferred from their emission
spectra. The underlying nonthermal particle acceleration (NTPA) processes have
traditionally been modeled with a Fokker-Planck (FP) diffusion-advection
equation in momentum space. In this paper, we directly test the FP framework in
ab-initio kinetic simulations of driven magnetized turbulence in relativistic
pair plasma. By statistically analyzing the motion of tracked particles, we
demonstrate the diffusive nature of NTPA and measure the FP energy diffusion
($D$) and advection ($A$) coefficients as functions of particle energy $\gamma
m_e c^2$. We find that $D(\gamma)$ scales as $\gamma^2$ in the high-energy
nonthermal tail, in line with 2nd-order Fermi acceleration theory, but has a
much weaker scaling at lower energies. We also find that $A$ is not negligible
and reduces NTPA by tending to pull particles towards the peak of the particle
energy distribution. This study provides strong support for the FP picture of
turbulent NTPA, thereby enhancing our understanding of space and astrophysical
plasmas.
