Statistics of power and efficiency for collisional Brownian engines

Collisional Brownian engines have attracted significant attention due to their simplicity, experimental accessibility, and amenability to exact analytical solutions. While previous research has predominantly focused on optimizing mean values of power and efficiency, the joint statistical properties of these performance metrics remain largely unexplored. Using stochastic thermodynamics, we investigate the joint probability distributions of power and efficiency for collisional Brownian engines, revealing how thermodynamic fluctuations influence the probability of observing values exceeding their respective mean maxima. Our conditional probability analysis demonstrates that when power fluctuates above its maximum mean value, the probability of achieving high efficiency increases substantially, suggesting fluctuation regimes where the classical power-efficiency trade-off can be probabilistically overcome. Notably, our framework extends to a broader class of engines, as the essential features of the statistics of the system are fully determined by the Onsager coefficients. Our results contribute to a deeper understanding of the role of fluctuations in Brownian engines, highlighting how stochastic behavior can enable performance beyond traditional thermodynamic bounds.