The available force in long-duration memory complex systems and its statistical physical properties

A new concept of the available force in long-duration memory complex systems is proposed. The relationship between the available force in different time intervals and the correlation parameters of complex systems is described. It is found that when the correlation parameters satisfy a determined condition, the trajectory where the velocity is divergent but the displacement is convergent can be well described and that the long-duration memory, anomalous diffusion, and q-Gaussian type distribution of complex systems can also be well described by the correlation parameters in different cases. In addition, by utilizing the velocity of time series randomly and analyzing its probability distribution of displacement, it is explained that when there exists a long-duration memory in complex systems, the fat-tail distributions will show up. The results obtained show that the relationship between the available force and the correlation parameters may be used to investigate the statistical physical properties in long-duration memory complex systems