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The result is justified for a wide family of time-scaling functions, making the FF protocols very flexible. We also revealed that the accelerated full cycle of the Carnot-like stochastic heat engine cannot be conceivable within the framework of the overdamped case, and the power and efficiency can be evaluated only when the momentum degree of freedom is taken into consideration.The paper considers the probability distributions of the nonlinear wave characteristics in nondispersive media that satisfy the Riemann- and the Kardar-Parisi-Z