Environmental-induced work extraction

Abstract: A measurement can extract work from an entangled, e.g., two-mode system. Here, we inquire the extracted work when no intellectual creature, like an ancilla/daemon, is present. When the monitoring is carried out by the environmental modes, that is when no measurement-apparatus is present, the measurement-basis becomes the coherent state. This implies a Gaussian measurement with a fixed strength $\lambda=1$. For two-mode Gaussian states, extracted work is already independent from the measurement outcome. After the strength is also fixed, this makes nature assign a particular amount of work to a given entanglement degree. Extracted work becomes the entanglement-degree times the entire thermal energy at low temperatures -- e.g., room temperature for optical modes. Environment, nature itself, converts entanglement to an ordered, macroscopic, directional~(kinetic) energy from a disordered, microscopic, randomized thermal energy. And the converted amount is solely determined by the entanglement.