  We introduce a new tool, the Deformed TBA (Deformed Thermodynamic Bethe
Ansatz), to analyze the monodromy problem of the cubic oscillator. The Deformed
TBA is a system of five coupled nonlinear integral equations, which in a
particular case reduces to the Zamolodchikov TBA equation for the 3-state Potts
model. Our method generalizes the Dorey-Tateo analysis of the (monomial) cubic
oscillator. We introduce a Y-system corresponding to the Deformed TBA and give
it an elegant geometric interpretation.
