Extracting work from two gravitational cat states

\n\nGravitational cat states in the context of gravity are superpositions of quantum states that exhibit macroscopically distinct gravitational fields. These states represent a unique blend of quantum mechanics and general relativity, providing insights into the behavior of quantum systems under gravitational influences. This study investigates the impact of thermal environments on the extractable work from gravitational cat states, which are quantum superpositions of distinct gravitational configurations. It aims to offer a comprehensive analysis of how temperature and gravitational interactions between states with masses m influence work extraction. The findings indicate that both an increase in temperature and the interactions between states reduce the amount of work that can be extracted from gravitational cat states, highlighting the delicate balance between thermal and gravitational effects in quantum systems.\n