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This paper investigates Rota-Baxter associative algebras of of arbitraryweights, that is, associative algebras endowed with Rota-Baxter operators ofarbitrary weights from an operadic viewpoint. Denote by $\RB$ the operad ofRota-Baxter associative algebras. A homotopy cooperad is explicitlyconstructed, which can be seen as the Koszul dual of $\RB$ as it is proven thatthe cobar construction of this homotopy cooperad is exactly the minimal modelof $\RB$. This enables us to give the notion of homotopy Rota-Baxterassociative algebras. The deformation complex of a Rota-Baxter associativealgebra and the underlying $L_\infty$-algebra structure over it are exhibitedas well.

The minimal model of Rota-Baxter operad with arbitrary weight