  The Boltzmann-Gibbs thermodynamic equilibrium state of charged particles
pitch-angle scattered by weak plasma waves is discussed. Degrees of freedom of
these waves play a fundamental role in constructing the grand canonical
ensemble. Via the gyro-resonance condition, fast particles have an inverse
break power-law spectrum for $ \varepsilon -\mu \ll T $, where $ \varepsilon $
is the particle energy, $ \mu $ is the chemical potential, $ T $ is the
temperature. The break energies are the rest energy and $ -\mu $. For $
\varepsilon \ll -\mu \ll T $, the energy spectral index $ \alpha $ is $ \delta
/2+1 $ and $ \delta +1 $ for non- and ultra-relativistic particles,
respectively, with $ \delta $ an effective fractal dimension of background
magnetic field lines. The spectral index for $ -\mu \ll \varepsilon \ll T $ is
$ \alpha +1 $. This thermal equilibrium scenario, combined with the leaky-box
model and cosmic-ray observations, seems to suggest that the Galactic magnetic
field is super-diffusive with $ \delta \approx 1.4 $.
