Thermodynamics of two aligned Kerr-Newman black holes

Using the notion of thermodynamic length, first law thermodynamics is consistently derived for two binary configurations equal Kerr-Newman black holes separated by a massless strut. Like in electrostatic systems Reissner-Nordstr\"om and stationary vacuum Kerr considered earlier, length $\ell$ turns out to be defined same simple formula $\ell=L\exp(\gamma_0)$, $L$ being coordinate strut $\gamma_0$ value metric function $\gamma$ on strut, which permits elaboration concise analytic form. The expression free energy case generic also proposed.