  We compute the Euclidean actions of a $d$-dimensional charged rotating black
brane both in the canonical and the grand-canonical ensemble through the use of
the counterterms renormalization method, and show that the logarithmic
divergencies associated with the Weyl anomalies and matter field vanish. We
obtain a Smarr-type formula for the mass as a function of the entropy, the
angular momenta, and the electric charge, and show that these quantities
satisfy the first law of thermodynamics. Using the conserved quantities and the
Euclidean actions, we calculate the thermodynamics potentials of the system in
terms of the temperature, angular velocities, and electric potential both in
the canonical and grand-canonical ensembles. We also perform a stability
analysis in these two ensembles, and show that the system is thermally stable.
This is commensurate with the fact that there is no Hawking-Page phase
transition for a black object with zero curvature horizon. Finally, we obtain
the logarithmic correction of the entropy due to the thermal fluctuation around
the equilibrium.
