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The Landauer-Butikker formalism is an important formalism to study mesoscopicsystems. Its validity for linear transport is well established theoretically aswell as experimentally. Akkermans et al [Phys. Rev. Lett. {\bf 66}, 76 (1991)]had shown that the formalism can be extended to study thermodynamic propertieslike persistent currents. It was earlier verified for simple one dimensionalsystems. We study this formula very carefully and conclude that it requiresreinterpretation in quasi one dimension. This is essentially because of thepresence of evanescent modes in quasi one dimension.

S-Matrix Formulation of Mesoscopic Systems and Evanescent Modes