We describe a new infinite family of multi-parameter functional equati
ons for the Rogers dilogarithm, generalizing Abel's and Euler's formul
as. They are suggested by the Thermodynamic Bethe Ansatz approach to t
he renormalization group flow of 2D integrable, ADE-related quantum fi
eld theories. The known sum rules for the central charge of critical f
ixed points can be obtained as special cases of these. We conjecture t
hat similar functional identities can be constructed for any rational
integrable quantum field theory with factorized S-matrix and support i
t with extensive numerical checks.