Nonanalytic contributions to the self-energy and the thermodynamics of two-dimensional Fermi liquids

We calculate the entropy of a two-dimensional Fermi liquid using a model with a contact interaction between fermions. We find that there are ${\mathit{T}}^2$ contributions to the entropy from interactions separate from those due to the collective modes. These ${\mathit{T}}^2$ contributions arise fron nonanalytic corrections to the real part of the self-energy which may be calculated from the leading-log dependence of the imaginary part of the self-energy through the Kramers-Kronig relation. We find no evidence of a breakdown in Fermi liquid theory in 2D and conclude that Fermi liquids in 2D are similar to 3D Fermi liquids.