This paper states the case for applying the conceptual and analytic tools associated with the study of entropy in physical systems to cognition, focusing on creative cognition. It is proposed that minds modify their contents and adapt to their environments to minimize psychological entropy: arousal-provoking uncertainty, which can be experienced negatively as anxiety, or positively as a wellspring for creativity (or both). Thus, intrinsically motivated creativity begins with detection of high psychological entropy material (e.g., a question or inconsistency), which provokes uncertainty and is arousal-inducing. This material is recursively considering from new contexts until it is sufficiently restructured that arousal dissipates and entropy reaches an acceptable level. Restructuring involves neural synchrony and dynamic binding, and may be facilitated by temporarily shifting to a more associative mode of thought. The creative outcome may similarly induce restructuring in others, and thereby contribute to the cultural evolution of more nuanced understandings. Thus, the concept of entropy could play a unifying role in cognitive science as a driver of thought and action, and in cultural studies as the driver of the creative innovations that fuel cultural evolution. The paper concludes with an invitation for cross-disciplinary exploration of this potential new arena of entropy studies.