  The paper develops a theoretical relationship between the polytropic index
and the temperature anisotropy that may characterize space plasmas. The
derivation is based on the correlation among the kinetic energies of particles
with velocities described by anisotropic kappa distributions. The correlation
coefficient depends on the effective dimensionality of the velocity
distribution function, having its shape determined by the temperature
anisotropies caused by the ambient magnetic field; on the other hand, the
effective dimensionality is directly dependent on the polytropic index. This
analysis leads to the connection between the correlation coefficient, effective
dimensionality of velocity space, and the polytropic index, with the ratio of
temperature anisotropy. Moreover, a data and statistical analysis is performed
to test the application of the theoretically developed model, in the solar wind
proton plasma near 1 AU. The derived theoretical relationship is in good
agreement with observations, showing that the lowest and classical value of the
adiabatic polytropic index occurs in the isotropic case, while higher indices
characterize anisotropic plasmas. Finally, possible extensions of the theory
considering (i) non-adiabatic polytropic behavior, and (ii) more general
distributions, are further discussed.
