Blind directions of linear response and the limits of finite-perturbation bounds on efficiency fluctuations

Thermodynamic uncertainty relations bound the fluctuations of time-antisymmetric currents. Stochastic efficiency is not one: a ratio of two odd quantities, it is even under path reversal, and for the conventional ratio $-W/Q_h$ no moment exists. We work with the exergetic ratio $η=W/(W+T_0S)$, whose