Cell-cell interaction dictates cell morphology and organization, which play a crucial role in the micro-architecture of tissues that guides their biological and mechanical functioning. Here, we investigate the effect of cell density on the responses of cells seeded on flat substrates using a novel statistical thermodynamics framework. The framework recognizes the existence of nonthermal fluctuations in cellular response and thereby naturally captures entropic interactions between cells in monolayers. In line with observations, the model predicts that cell area and elongation decrease with increasing cell seeding density-both are a direct outcome of the fluctuating nature of the cellular response that gives rise to enhanced cell-cell interactions with increasing cell crowding. The modeling framework also predicts the increase in cell alignment with increasing cell density: this cellular ordering is also due to enhanced entropic interactions and is akin to nematic ordering in liquid crystals. Our simulations provide physical insights that suggest that entropic cell-cell interactions play a crucial role in governing the responses of cell monolayers.