Thermodynamics of Multiple Two-body Systems with Long-range Correlation

We aim to study thermodynamics of multiple two-body systems with long-range correlation using non-extensive statistics. Long-range correlation will cause multiple systems in anomalous diffusion. We consider the influence of long-range correlation as a background noise effect on a two-body system. We solve probability and entropy equations of a two-body system to obtain the temperature and distance dependence of the non-extensive parameter. The result shows the long-range correlation changes the system's entropy and energy. The more strongly is the system bounded, the less its energy is affected by the long-range correlation. Moreover, the anomalous diffusion approaches Brown motion with increasing temperature. This will help to understand how nonlinear field affects thermodynamics of a system.