Which has lower entropy: a protein monomer or a protein dimer?

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Entropy reflects how many ways a system can arrange itself. A single protein monomer in solution has many translational, rotational, and conformational possibilities, so it enjoys a relatively large number of accessible microstates. When two monomers come together to form a dimer, they become a single unit with a defined interface and restricted relative motion. This ordering reduces translational and rotational freedom and often limits conformational options, lowering the number of accessible microstates. The net result is a decrease in entropy upon dimer formation, so the dimer has lower entropy than the monomer. Solvent effects can modulate how big that drop is, but the general trend remains that association lowers entropy.