Apparent violations of the second law in the quantum-classical dynamics of interacting levitated nanoparticles

Random exchanges of energy arise naturally in stochastic systems. As a consequence, apparent violations of the second law of thermodynamics can occur at the trajectory level, even though the law holds true on average. Here, we investigate the occurrence of these apparent violations-termed free lunches-in a quantum-classical system comprised of levitated nanoparticles exchanging energy via the Coulomb interaction. We consider different initial states for the quantum system, and how these exert work and fluctuations upon the classical particle affecting the probability of free lunches. With that, we initiate the study of hybrid quantum-classical systems through the lens of stochastic thermodynamics.