Some Details of Statistical Mechanics of Many-Body Systems in the Presence of a Measurable Minimal Length

Different approaches to quantum gravity proposal such as string theory, doubly special relativity, and also black holes physics, all commonly address the existence of a minimal measurable length of the order of the Planck length. One way to apply the minimal length is changing the Heisenberg algebra in the phase space which is known as the generalized uncertainty principle. It is essential to apply this feature on the statistical mechanics of many body systems in the presence of a measurable minimal length scale in order to see the roles of this natural cutoff on physical phenomena. In this paper, some details of statistical mechanics of many body systems that have not been studied carefully in literature are studied in the presence of minimal length scale. The issues such as isomerization, the Liouville theorem, virial theorem and equipartition theorem are studied in this setup with details and the results are explained thoroughly.