  The sine-Gordon Y-systems and those of the minimal $M_{p,q}+\phi_{13}$ models
are determined in a compact form and a correspondence between the rational
numbers and a new infinite family of multi-parameter functional equations for
the Rogers dilogarithm is pointed out. The relation between the TBA-duality and
the massless RG fluxes in the minimal models recently conjectured is briefly
discussed.
