A polytropic process describes the transition of a fluid from one state to another through a specific relationship between the fluid density and temperature. The value of the polytropic index that governs this relationship determines the heat transfer and the effective degrees of freedom during a specific process. In this study, we analyze solar wind proton plasma measurements, obtained by the Faraday cup instrument on board the Parker Solar Probe. We examine the large-scale variations of the proton plasma density and temperature within the inner heliosphere explored by the spacecraft. We then address the polytropic behavior in the density and temperature fluctuations in short time intervals, which we analyze in order to derive the effective polytropic index of small-scale processes. The large-scale variations of the solar wind proton density and temperature, which are associated with the plasma expansion into the heliosphere, follow a polytropic model with a polytropic index ∼5/3. On the other hand, the short-scale fluctuations, which are potentially associated with turbulence, follow a model with a larger polytropic index. We investigate possible correlations between the polytropic index of short-scale fluctuations and the plasma speed, plasma β, and the magnetic field direction. We discuss candidate mechanisms leading to this behavior including energy transfer and possible mechanisms restricting the effective particle degrees of freedom at smaller scales.