Single-cell omics is transforming our understanding of cell biology and disease, yet the systems-level analysis and interpretation of single-cell data faces many challenges. In this Perspective, we describe the impact that fundamental concepts from statistical mechanics, notably entropy, stochastic processes and critical phenomena, are having on single-cell data analysis. We further advocate the need for more bottom-up modelling of single-cell data and to embrace a statistical mechanics analysis paradigm to help attain a deeper understanding of single-cell systems biology.