Thermodynamics of accelerating and supersymmetric <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>AdS</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math> black holes

We study the thermodynamics of ${\mathrm{AdS}}_{4}$ black hole solutions Einstein-Maxwell theory that are accelerating, rotating, and carry electric magnetic charges. focus on class for which horizon is a spindle can be uplifted regular Sasaki-Einstein spaces to give $D=11$ supergravity free from conical singularities. use holography calculate Euclidean on-shell action define set conserved charges rise first law. identify complex locus supersymmetric nonextremal solutions, defined through an analytic continuation parameters, upon we obtain simple expression action. A Legendre transform this combined with reality constraint then leads Bekenstein-Hawking entropy extremal holes.