The second law of thermodynamics imposes limits on energy conversion, such as the Carnot bound. Apparent violations in active baths often arise from incomplete accounting of the reservoir's energetics. By treating active noise as an explicit degree of freedom in a Brownian gyrator model, we show that entropy production remains non-negative and the Carnot limit is preserved. This study demonstrates that properly accounting for active fluctuations as distinct thermodynamic components upholds fundamental principles.
(Left) Diagram of a 2D AOUP gyrator. Active noise can be treated as part of the heat baths. (Right) Diagram of a 4D white noise gyrator. The active noise can be treated as a particle immersed in two distinct white-noise baths acting on the colloidal bead.
