  We analyze proton bulk parameters derived from Ulysses observations and
investigate the polytropic behavior of solar wind protons over a wide range of
heliocentric distances and latitudes. The large-scale variations of the proton
density and temperature over heliocentric distance, indicate that plasma
protons are governed by sub-adiabatic processes (polytropic index $\gamma$ <
5/3), if we assume protons with three effective kinetic degrees of freedom.
From the correlation between the small-scale variations of the plasma density
and temperature in selected sub-intervals, we derive a polytropic index
$\gamma$ ~ 1.4 on average. Further examination shows that the polytropic index
does not depend on the solar wind speed. This agrees with the results of
previous analyses of solar wind protons at ~ 1 au. We find that the polytropic
index varies slightly over the range of the heliocentric distances and
heliographic latitudes explored by Ulysses. We also show that the homogeneity
of the plasma and the accuracy of the polytropic model applied to the
data-points vary over Ulysses orbit. We compare our results with the results of
previous studies which derive the polytropic index of solar wind ions within
the heliosphere using observations from various spacecraft. We finally discuss
the implications of our findings in terms of heating mechanisms and the
effective degrees of freedom of the plasma protons.
