Active noise diminishes rather than enhances the performance of a Brownian gyrator

Yi-Hung Liao^1*, Wenqi Lin¹, Pik-Yin Lai¹, Yonggun Jun¹

¹Department of Physics, National Central University, Taoyuan, Taiwan

* Presenter:Yi-Hung Liao, email:yihungliao@ncu.edu.tw

The efficiency of a heat engine is upper bound by the Carnot limit based on The Second Law of Thermodynamics. Recent theoretical studies show the promise of higher output work and higher-than-Carnot-limit efficiency for a heat engine in an active bath than in a thermal one [1]. While the concept of “extra unconventional entropy production (EP)” is proposed to validate this phenomenon [1], there has also been an effort attempting to circumvent this violation of the thermodynamic second law by involving excess EP [2]. In this work, by treating a Brownian gyrator in a hybrid bath including both 2D white noise and an active (Ornstein-Uhlenbeck) noise as one that is subject to a 4D white noise, we find that the gyrator no longer functions as a heat engine in the “working region” as previously claimed. Moreover, the original thermodynamic second law still holds without violating Carnot efficiency and the thermodynamic uncertainty relation (TUR). We derive analytical solutions of the energetics for the 4D white noise gyrator and provide numerical and experimental verification using a colloidal Brownian gyrator manipulated by an optical feedback trap. Our results suggest the augmented performance in an active bath originates from the incorrect inclusion of the energy generated by the coupling of active noise and position as work. Detailed discussion will be given.

Keywords: Brownian gyrator, active noise, thermodynamic uncertainty relation