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Comment on "Wave-scattering formalism for thermal conductance in thin wires with surface disorder"

In their calculations based on the Landauer transport equation, Akguc and Gong [Phys. Rev. B 80, 195408 (2009)] obtained an expression for the heat conductance of a quantum wire valid in the ballistic regime and in the limit of vanishing temperature difference between reservoirs. Their result appears to be different from the one reported in the previous paper of Rego and Kirczenow [Phys. Rev. Lett. 81, 232 (1998)], which led them to argue that their new result was the correct one. We show here that, in fact, both results are correct since different definitions for the dilogarithm function were used in those papers. Hence, comparisons between these two results should be done with care.