We propose Medical Entity Definition-based Sentence Embedding (MED-SE), a novel unsupervised contrastive learning framework designed for clinical texts, which exploits the definitions of medical entities. To this end, we conduct an extensive analysis of multiple sentence embedding techniques in clinical semantic textual similarity (STS) settings. In the entity-centric setting that we have designed, MED-SE achieves significantly better performance, while the existing unsupervised methods including SimCSE show degraded performance. Our experiments elucidate the inherent discrepancies between the general- and clinical-domain texts, and suggest that entity-centric contrastive approaches may help bridge this gap and lead to a better representation of clinical sentences.