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The physical relevance of the thermodynamic volumes of AdS black holes to thegravity duals of quantum complexity was recently argued by Couch et al. In thispaper, by generalizing the Wald-Iyer formalism, we derive a geometricexpression for the thermodynamic volume and relate its product with thethermodynamic pressure to the non-derivative part of the gravitational actionevaluated on the Wheeler-DeWitt patch. We propose that this action provides analternative gravity dual of the quantum complexity of the boundary theory. Werefer this to "complexity=action 2.0" (CA-2) duality. It is significantlydifferent from the original "complexity=action" (CA) duality as well as the"complexity=volume 2.0" (CV-2) duality proposed by Couch et al. The latterpostulates that the complexity is dual to the spacetime volume of theWheeler-DeWitt patch. To distinguish our new conjecture from the variousdualities in literature, we study a number of black holes inEinstein-Maxwell-Dilation theories. We find that for all these black holes, theCA duality generally does not respect the Lloyd bound whereas the CV-2 dualityalways does. For the CA-2 duality, although in many cases it is consistent withthe Lloyd bound, we also find a counter example for which it violates the boundas well.

On the Noether charge and the gravity duals of quantum complexity