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Interpersonally shared physiological dynamics are increasingly argued to underlie rapport, empathy, and even team performance. Inspired by the model of interpersonal synergy, we critically investigate the presence, temporal development, possible mechanisms and impact of shared interpersonal heart rate (HR) dynamics during individual and collective creative LEGO® construction tasks. In Study 1 we show how shared HR dynamics are driven by a plurality of sources, including task constraints and behavioral coordination. Generally, shared HR dynamics are more prevalent in individual trials (involving participants doing the same things) than in collective ones (involving participants taking turns and performing complementary actions). However, when contrasted against virtual pairs, collective trials display more stable shared HR dynamics suggesting that online social interaction plays an important role. Furthermore, in contrast to individual trials, shared HR dynamics are found to increase across collective trials. Study 2 investigates which aspects of social interaction might drive these effects. We show that shared HR dynamics are statistically predicted by interpersonal speech and building coordination. In Study 3, we explore the relation between HR dynamics, behavioral coordination, and self-reported measures of rapport and group competence. Although behavioral coordination predicts rapport and group competence, shared HR dynamics do not. Although shared physiological dynamics were reliably observed in our study, our results warrant not to consider HR dynamics a general driving mechanism of social coordination. Behavioral coordination—on the other hand—seems to be more informative of both shared physiological dynamics and collective experience.