  Previously the five dimensional $S^1$-rotating black rings have been
superposed in a concentric way by some solitonic methods, and regular systems
of two $S^1$-rotating black rings were constructed by the authors and then
Evslin and Krishnan (we called these solutions "black di-rings"). In this place
we show some characteristics of the solutions of five dimensional black
di-rings, especially in thermodynamic equilibrium. After the summary of the
di-ring expressions and their physical quantities, first we comment on the
equivalence of the two different solution sets of the black di-rings. Then the
existence of thermodynamic black di-rings is shown, in which both isothermality
and isorotation between the inner black ring and the outer black ring are
realized. We also give detailed analysis of peculiar properties of the
thermodynamic black di-ring including discussion about a certain kind of
thermodynamic stability (instability) of the system.
