Polytropic index and thermodynamic behaviour of the central plasma sheet near lunar distances

{In addition to making near-Earth observations{,} the THEMIS / ARTEMIS mission is uniquely positioned at lunar distance, in the deep magnetotail, reaching distances of 60 RE and further. This vantage point allows ARTEMIS to access plasma sheets and measure entropy evolution across convective channels, plasma flow gradients, reconnection outflows, flow burst timing, and dipolarization fronts. In this study, we examine the thermodynamic behavior of the central plasma sheet (CPS) near-Earth and at the distant magnetotail, across the northern and southern hemispheres, during dusk and dawn sides, and also during geomagnetic quiet and active conditions. The specific entropy evolution and the mechanisms of the heating and cooling process during mass and energy transport in the Earth's plasma sheet (PS) are also investigated. We use 10 years of THEMIS-C/ ARTEMIS-P2 spacecraft data during CPS crossings, and the polytropic index relation of {2024ApJ…966..142D}. Our results show that (1) the specific entropy and the polytropic index value varies radially in the CPS; (2) the thermodynamic process that takes place in the CPS at lunar distance is more likely a subadiabatic process; (3) near lunar distance, the northern and southern hemispheres, during quiet and active geomagnetic conditions, display nearly the same polytropic index. The results of this study can be used for modeling and simulation of magnetospheric substorms and also have implications {relevant} to the pressure catastrophe problem in substorm models}.