  At the heart of quantum thermodynamics lies a fundamental question about what
is genuine "quantum" in quantum heat engines and how to seek this quantumness,
so that thermodynamical tasks could be performed more efficiently compared with
classical protocols. Here, using the concept of $P$-representability, we define
a function called classicality, which quantifies the degree of non-classicality
of bosonic modes. This function allows us to explore the role of
non-classicality in quantum heat engines and design optimal protocols for work
extraction. For two specific cycles, a quantum Otto and a generalised one, we
show that non-classicality is a fundamental resource for performing
thermodynamic tasks more efficiently.
