  The Harada-Sasa equality elegantly connects the energy dissipation rate of a
moving object with its measurable violation of the Fluctuation-Dissipation
Theorem (FDT). Although proven for Langevin processes, its validity remains
unclear for discrete Markov systems whose forward and backward transition rates
respond asymmetrically to external perturbation. A typical example is a motor
protein called kinesin. Here we show generally that the FDT violation persists
surprisingly in the high-frequency limit due to the asymmetry, resulting in a
divergent FDT violation integral and thus a complete breakdown of the
Harada-Sasa equality. A renormalized FDT violation integral still well predicts
the dissipation rate when each discrete transition produces a small entropy in
the environment. Our study also suggests a new way to infer this perturbation
asymmetry based on the measurable high-frequency-limit FDT violation.
