The efficiency of a linear heat engine in contact with the active bath

Our experiment shows that an introduction of time-correlated Ornstein-Uhlenbeck (OU) noise to a stochastic heat engine can elevate engine efficiency beyond the Carnot limit set by classical thermodynamics. We adopt a Brownian gyrator as a model system in which a water-immersed Brownian particle is constrained in a two-dimensional harmonic potential and subject to distinct effective temperatures and nonconservative coupling forces in orthogonal axes. Proper choice of the coupling force strength allows the gyrator to harvest work from its environments, operating as a heat engine. Compared with a counter-passive heat engine, thermodynamics currents (work and heat rates) are enhanced. Moreover, under some specific coupling force strengths, engine efficiency goes beyond the Carnot limit with non-zero power. We will discuss the influences of OU noise on the trade-off relation between the fluctuations of thermodynamic currents and the entropic cost.