Quantum entanglement and extractable work for Gaussian states.

The study of quantum thermodynamics aims to elucidate the role played by quantum principles in the emergent features of quantum thermodynamic processes. Specifically, it is of fundamental importance to understand how quantum correlation among different parties enables thermodynamic features distinguishable from those arising in classical thermodynamics. In this work, we investigate the relation between extractable work and quantum correlations for two-mode Gaussian states. We examine the change in local energy occurring at one party due to a Gaussian measurement performed on the other in relation to the quantum correlations of two-mode states classified as separable, entangled, and steerable states. Our analysis reveals a clear quantitative difference in the extractable work, depending on the class of states to which the two-mode state belongs.