We show that Tsallis and multicanonical statistical mechanics are equivalent under specific conditions and that they describe a system strongly coupled to a heat bath. The concept of the strong coupling to a heat bath, in which energy fluctuation is larger than that in the canonical ensemble [J. Chem. Phys. 119, 7075 (2003)], plays a key role in relating Tsallis formalism to multicanonical formalism. The equivalence between these formalisms allows us to obtain an appropriate q parameter in the Tsallis algorithm to enhance the sampling in the phase space in a manner similar to the multicanonical algorithm. An enhanced sampling in the configurational space by use of the strong coupling formalism is demonstrated in a Lennard-Jones fluid.