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We present a tidal model for treating the rotational evolution in the generalthree-body problem with arbitrary viscosities, in which all the masses areconsidered to be extended and all the tidal interactions between pairs aretaken into account. Based on the creep tide theory, we present the set ofdifferential equations that describes the rotational evolution of each body, ina formalism that is easily extensible to the N tidally-interacting bodyproblem. We apply our model to the case of a circumbinary planet and use aKepler-38 like binary system as a working example. We find that, in this lowplanetary eccentricity case, the most likely final stationary rotation state isthe 1:1 spin-orbit resonance, considering an arbitrary planetary viscosityinside the estimated range for the solar system planets. We derive analyticalexpressions for the mean rotational stationary state, based on high-order powerseries of the semimajor axes ratio a1 /a2 and low-order expansions of theeccentricities. These are found to reproduce very accurately the mean behaviourof the low-eccentric numerical integrations for arbitrary planetary relaxationfactors, and up to a1/a2 \sim 0.4. Our analytical model is used to predict thestationary rotation of the Kepler circumbinary planets and find that most ofthem are probably rotating in a sub-synchronous state, although the synchronyshift is much less important than the one estimated in Zoppetti et al. (2019,2020). We present a comparison of our results with those obtained with theConstant Time Lag and find that, unlike what we assumed in our previous works,the cross torques have a non-negligible net secular contribution, and must betaken into account when computing the tides over each body in anN-extended-body system from an arbitrary reference frame. These torques arenaturally taken into account in the creep theory.

Creep Tide Model for the 3-Body Problem. The rotational evolution of a circumbinary planet