| Summary: | This paper improves our understanding of the interplay of the proton plasma turbulent heating sources of the expanding solar wind in the heliosphere. Evidence is shown of the connections between the polytropic index, the rate of the heat absorbed by the solar wind, and the rate of change of the turbulent energy, which heats the solar wind in the inner and outer heliosphere. In particular, we: (i) show the theoretical connection of the rate of a heat source, such as the turbulent energy, with the polytropic index and the thermodynamic process; (ii) calculate the effect of the pick-up protons in the total proton temperature and the relationship connecting the rate of heating with the polytropic index; (iii) derive the radial profiles of the solar wind heating in the outer and inner heliosphere; and (iv) use the radial profile of the turbulent energy in the solar wind proton plasma in the heliosphere, in order to show its connection with the radial profiles of the polytropic index and the heating of the solar wind.
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