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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. [ABSTRACT FROM AUTHOR]

The scattering cross-section of electrons in noble gas atoms exhibits the minimum value at electron energies of approximately 1 eV. This is the Ramsauer-Townsend effect. In this letter, we study the Ramsauer-Townsend effect in the presence of both the minimal observable length and the maximal momentum (originating from doubly special theories) through the generalized uncertainty principle. [ABSTRACT FROM AUTHOR]