Abdalla, M. C.B.Bytsenko, A. A.Guimarães, M. E.X. [UNESP]2022-04-282022-04-282004-01-01Physical Review D - Particles, Fields, Gravitation and Cosmology, v. 69, n. 6, p. 6-, 2004.1550-23681550-7998http://hdl.handle.net/11449/224583We discuss the matching of the BPS part of the spectrum for a (super)membrane, which gives the possibility of getting the membrane’s results via string calculations. In the small coupling limit of M theory the entropy of the system coincides with the standard entropy of type IIB string theory (including the logarithmic correction term). The thermodynamic behavior at a large coupling constant is computed by considering M theory on a manifold with a topology [Formula Presented] We argue that the finite temperature partition functions (brane Laurent series for [Formula Presented] associated with the BPS p-brane spectrum can be analytically continued to well-defined functionals. It means that a finite temperature can be introduced in brane theory, which behaves like finite temperature field theory. In the limit [Formula Presented] (point particle limit) it gives rise to the standard behavior of thermodynamic quantities. © 2004 The American Physical Society.6engArtigo10.1103/PhysRevD.69.0640022-s2.0-2342420379