Stochastic heat engines beyond a unique definition of temperature

When Carnot and Stirling initially conceptualized heat engines, temperature unambiguously represented our everyday perception of cold and hot. However, as this energy scale is expanded to measure the strength of noise in general nonequilibrium heat baths, such as those consisting of bacteria or active particles, it takes on different definitions and connotations. This raises a fundamental question of whether and how thermodynamic conclusions beyond a unique definition of temperature would deviate from our conventional understanding. To address this inquiry, we investigate a colloidal Stirling engine governed by a large number of stochastic dynamical systems. Within experimentally accessible parameter values, we discover certain exceptional active engines that can outperform their passive counterpart, as notably claimed in a recent experiment involving a bacterial bath. Our analysis shows that such heightened performance can be attributed to either a restoring effect in noise or a significant dissipation kernel. The revealed influence of active baths on Stirling efficiency provides further insights into their impact on maximum power output, Carnot efficiency, and Curzon-Alhborn efficiency. The finding elucidates the origins of exceptional performance in stochastic heat engines, offers strategies for harvesting energies from active noises, and sheds light on the effects of nonequilibrium temperature in stochastic thermodynamics.