Hierarchical Onsager symmetries in adiabatically driven linear irreversible heat engines

In existing linear response theories for adiabatically driven cyclic heat engines, Onsager symmetry is identified only phenomenologically, and a relation between global local coefficients, defined over one cycle at any instant of cycle, respectively, not derived. To address this limitation, we develop theory the speed changing parameters temperature differences in generic Gaussian engines obeying Fokker--Planck dynamics. We establish hierarchical relationship relations, ones, cycle. This yields detailed expression coefficients terms coefficients. Moreover, derive an efficiency bound, which tighter than Carnot irreversible based on Finally, demonstrate application using simplest stochastic Brownian engine model.