The sine-Gordon Y-systems and those of the minimal M(p,q) + phi(13) mo
dels are determined in a compact form and a correspondence between the
rational numbers and a new infinite family of multi-parameter functio
nal equations for the Rogers dilogarithm is pointed out. The relation
between the TBA duality and the massless RG fluxes in the minimal mode
ls recently conjectured is briefly discussed.