2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/186207The physical version and equilibrium state version of the first law of thermodynamics for a black object consisting of n-dimensional charged stationary axisymmetric black hole surrounded by $a$ black rings, the so-called black Saturn was derived. The general setting for our derivation is n-dimensional dilaton gravity with p + 1 strength form fields.9 pages, RevTex, to be published in Phys.Rev.D15High Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext