  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.
