Current fluctuation theorem for excess entropy of active cyclic systems

Active cyclic systems are paradigmatic models for studying small systems with large fluctuations within the framework of stochastic thermodynamics. A 2022 study showed that the excess entrop — a component of the total entropy production, offers distinct advantages over total entropy production when analyzing active cyclic heat engines. That work further demonstrated that a decomposition of the excess entropy contains an information-theoretic term I, which plays a crucial role in the formulation of the second law for these active cyclic systems. In our recent work, we prove a fluctuation theorem for the currents associated with the excess entropy based on this decomposition, employing the mathematical framework of large-deviation theory. This fluctuation theorem provides a cornerstone for developing a linear-response theory for active cyclic systems, including a fluctuation–dissipation relation and Onsager reciprocal relations.