Statistical mechanical description of galaxy clusters in strong gravitational fields

In this paper, we utilize a modified gravity theory that yields an enhanced clustering parameter at intermediate distances. We formulate the thermodynamic properties of galaxy clusters through a statistical mechanical framework. By solving the partition function for a strongly gravitating system within the context of the modified gravitational potential, we enable the calculation of various thermodynamic potentials. Additionally, we introduce a modified clustering parameter that demonstrates enhanced clustering effects at intermediate distances. Also, the probability distribution function is developed under the modified gravitational potential. A comparison between the data and theory is also made. We further evaluate the model by comparing the results with data from SDSS-III, which enables us to identify the relevant parameters.