  We describe a new infinite family of multi-parameter functional equations for
the Rogers dilogarithm, generalizing Abel's and Euler's formulas. They are
suggested by the Thermodynamic Bethe Ansatz approach to the Renormalization
Group flow of 2D integrable, ADE-related quantum field theories. The known sum
rules for the central charge of critical fixed points can be obtained as
special cases of these. We conjecture that similar functional identities can be
constructed for any rational integrable quantum field theory with factorized
S-matrix and support it with extensive numerical checks.
